https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVsohD4Sxlv_DRdoO-oPe86LWxKtDq4BkSl2d5fpkargXIyIdP7hUqkS5PhIitTswcgbYIy3-Fsf7zxlWbKqByiDh9hmkvVWxyRJP4gMfCwi1I-EVIQug8pHxDgaPluv-EuebseXT3Tnra/s1600-h/dodec+lines+on+earth+2.GIF
Plane-face dodecahedron (left) to spherical icosadodecahedron (center & right), great circles, small circles on pent faces may be ocean/air gyres, polar axis vs solar-lunar tides
http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/Foldout/TIcosahedron/Img/ticGn-s128-z5.eos.png
A truncated icosahedron globe
Showing posts with label sphere. Show all posts
Showing posts with label sphere. Show all posts
Thursday, March 1, 2012
Saturday, October 15, 2011
Videos
Incredible videos: mussel hunting under ice during low tide, others
http://www.youtube.com/watch_popup?v=Z0qGvC3vqaA
Amazing pendulum waves of Mach:
http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80863&pageContentId=icb.pagecontent341734&state=maximize&view=view.do&viewParam_name=indepth.html#a_icb_pagecontent341734
http://www.youtube.com/watch_popup?v=Z0qGvC3vqaA
Amazing pendulum waves of Mach:
http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80863&pageContentId=icb.pagecontent341734&state=maximize&view=view.do&viewParam_name=indepth.html#a_icb_pagecontent341734
Monday, March 22, 2010
Algebra in Wonderland?
Brief moment of math:
"The word “algebra,” De Morgan said in one of his footnotes, comes from an Arabic phrase he transliterated as “al jebr e al mokabala,” meaning restoration and reduction".
Was Lewis Carrols' Alice in Wonderland a satire of the new math of the time period?
NY Times article
Donald Duck in Mathmagic land: Disney cartoon movie from 1959
http://en.wikipedia.org/wiki/Donald_in_Mathmagic_Land
video short of film
http://www.kheper.net/topics/theoryofeverything/Reflexive.htm
h/t Kirby U @ synergeo
-
Synergetics
646.18 Atoms dislodged from the outer layer of the omniintermagnetized ball bearings would always roll around on one another to relocate themselves in some closest- packing array, with any two mass-interattracted atoms being at least in tangency. When another dynamic-spherical-domain atom comes into closest-packing tangency with the first two, the mutual interattractiveness interrolls the three to form a triangle. Three in a triangle produce a "planar" pattern of closest packing. When a fourth ball bearing lodges in the nest formed between and atop the first three, each of the four balls then touches three others simultaneously and produces a tetrahedron having a concave-faceted void within it. In this tetrahedral position, with four-dimensional symmetry of association, they are in circumferential closest packing. Having no mutual sphere, they are only intercircumferentially mass-interattracted and cohered: i.e., gravity alone coheres them, but gravity is hereby seen experimentally to be exclusively circumferential in interbonding.
646.19 With further spherical atom additions to the initial tetrahedral aggregate, the outermost balls tend to roll coherently around into asymmetrical closest-packing collections, until they are once more symmetrically stabilized with 12 closest packing around one and as yet exercising their exclusively intercircumferential interattractiveness, bound circumferentially together by four symmetrically interacting circular bands, whereby each of the 12 surrounding spheres has four immediately adjacent circumferential shell spheres interattracting them circumferentially, while there is only one central nuclear ball inwardly__i.e., radially attracting each of them. In this configuration they form the vector equilibrium.
What Bucky didn't address there is that any spherical configuration (with any number of spheres) produces a geometrical nucleus, but the surface area (number of surface facets) determines if the nucleus is vertexial like the VE (sometimes defined as a small rhombic dodeca) or skeletal polyhedral like the star tetra, star octa, star icosa core polyhedra.
"The word “algebra,” De Morgan said in one of his footnotes, comes from an Arabic phrase he transliterated as “al jebr e al mokabala,” meaning restoration and reduction".
Was Lewis Carrols' Alice in Wonderland a satire of the new math of the time period?
NY Times article
Donald Duck in Mathmagic land: Disney cartoon movie from 1959
http://en.wikipedia.org/wiki/Donald_in_Mathmagic_Land
video short of film
http://www.kheper.net/topics/theoryofeverything/Reflexive.htm
h/t Kirby U @ synergeo
-
Synergetics
646.18 Atoms dislodged from the outer layer of the omniintermagnetized ball bearings would always roll around on one another to relocate themselves in some closest- packing array, with any two mass-interattracted atoms being at least in tangency. When another dynamic-spherical-domain atom comes into closest-packing tangency with the first two, the mutual interattractiveness interrolls the three to form a triangle. Three in a triangle produce a "planar" pattern of closest packing. When a fourth ball bearing lodges in the nest formed between and atop the first three, each of the four balls then touches three others simultaneously and produces a tetrahedron having a concave-faceted void within it. In this tetrahedral position, with four-dimensional symmetry of association, they are in circumferential closest packing. Having no mutual sphere, they are only intercircumferentially mass-interattracted and cohered: i.e., gravity alone coheres them, but gravity is hereby seen experimentally to be exclusively circumferential in interbonding.
646.19 With further spherical atom additions to the initial tetrahedral aggregate, the outermost balls tend to roll coherently around into asymmetrical closest-packing collections, until they are once more symmetrically stabilized with 12 closest packing around one and as yet exercising their exclusively intercircumferential interattractiveness, bound circumferentially together by four symmetrically interacting circular bands, whereby each of the 12 surrounding spheres has four immediately adjacent circumferential shell spheres interattracting them circumferentially, while there is only one central nuclear ball inwardly__i.e., radially attracting each of them. In this configuration they form the vector equilibrium.
What Bucky didn't address there is that any spherical configuration (with any number of spheres) produces a geometrical nucleus, but the surface area (number of surface facets) determines if the nucleus is vertexial like the VE (sometimes defined as a small rhombic dodeca) or skeletal polyhedral like the star tetra, star octa, star icosa core polyhedra.
Friday, February 12, 2010
interim
"Every physical body has four basic sides, or four comers: two points alone are only collinear, and three are only coplanar; not until there are four comers can the property of spatial existence be recognized. As a result, any physical body must be held at four noncoplanar points (triangulated distally), with three torque restraints at each point (triangulated locally), in order to be stabilized.
There are four fundamental corners in every system, and each must be triangulated: 4 × 3 = 12. Thus there are twelve degrees of freedom, tetrahedrally organized." Amy Edmondson, A Fuller Explanation, Re. R. Buckminster Fuller, vector equilibrium
Relative Volume Table: (tetra volumes) | (cube volumes)
Icosa = 18.51 tv +
Vector edge Cube = 8.49 tv =
Icosa + Vector edge Cube = 27 tv -
Vector diagonal Cube = 3 tv (2 small duotets) =
2F lattice Cube = 24 tv (2 big duotets) -
Octa = 4 tv =
Star Icosa ext = 20 tv or
Cubocta = 20 tv + 8 ext tetra =
Star Cubocta Cube = 28 tv + 6 ext sq pyramids =
Cmpd Cubocta = 40 tv - 8 ext tetra =
Superocta = 6 octa & 8 tetra = 32 tv
compound of (1st stellation of) cube & octahedron (not star cubocta)
Cumulation: tet, octa, cube, icosa, dodeca can be cumulated 4 times
CUMULATION
(Cube & tet can't be stellated but both can be cumulated)
tetra, triakis tetra, cube, 12-faced star deltahedron (star tetra)
cube, tetrakis hexahedron, rhomb dodeca, 24 face star deltahedron (star cube)
octa, sm triakis octa, stella octangula/duotet (star octa)
star tetra, star octa (domain net of cubocta), star icosa
Now excluding the nucleic polyhedron volume:
View of surface tets as skeletal structure, equi length struts
Star Tet: nuc tet void, 4 tets, 6 circ + 12 ext struts = 18
Star Octa: nuc octa void, 8 tets, 12 circ + 24 ext struts = 36
Star Icosa: nuc icosa void, 20 tets, 30 circ + 60 ext struts = 90
I think the star tetra, star octa and star icosa qualify as 'VE', if the central polyhedra (reg tet, reg octa, reg icosa) is considered to be the nucleus. All the connecting vectors are same length AFAICT. Eg. the star icosa has all equal length vectors and has no centroid vectors (which would be a different length). So you need to specify which VE:
VE cubocta
VE star tetra
VE star octa
VE star icosa
The star tetra has 12 face planes
Multiplication by division: http://synergeticists.org/synergetics/plates/figs/plate03.html
Noting Kirby's & Alan's relative volume tables here:
math
Eschers solid
The volume of the cuboctahedron is 5/6 of that of the enclosing cube and 5/8 of that of the enclosing octahedron. The cuboctahedron shares its edges and vertex arrangement with two nonconvex uniform polyhedra: the cubohemioctahedron (having the square faces in common) and the octahemioctahedron (having the triangular faces in common).
I suggest adding one more, some star polyhedra with identical regular tetrahedra, the internal central polyhedron is a void*, since the external tetras produce the structure, so no additional struts required:
star tetra: 4 tetras (star tet - tet nucleus)
star octa: 8 tetras (duotet - octa nucleus)
star cubocta: 8 tetras (cube - cubocta nucleus)
=====================
star icosa: 20 tetras (4 + 8 + 8) * jitterbug transformation
*These exclude the nuclear polyhedron, since it is a void built by the exoskeleton of structural tets and overlapped struts are unnecessary.
I haven't checked if the orientation of the 20 tets of the star icosa match with those of the others, or if they need to be rotated or jitterbugged to fit the icosa.
compound cubocta & 120 cell
What can fit into an icosa? a tet. an octa. a star tet? a star octa?
unknown.
rhombic dodeca (cube with pyramidal faces combine coplanar pairs of triangles into rhombi) rhomdodeca from cube+6pyramid (differs from star cube with noncoplanar pairs of triangles)
star rhombic dodeca & star octa:
star vol
C60 Carbon buckyball fullerene: 60 vertices divided into 12 pentagon sets; 32 faces of 12 pentas and 20 hexas, 90 edges of 60 pentagonal edges (single bonds)and 30 hexagonal edges (double bonds), each hexagon has alternating single and double bonds. Dual of truncated icosahedron C60 with 32 faces and 60 vertices is the pentakis dodecahedron (triangulated C60) of 60 faces and 32 vertices.
syn
1033.53 The vector equilibrium jitterbug provides the articulative model for demonstrating the always omnisymmetrical, divergently expanding or convergently contracting intertransformability of the entire primitive polyhedral hierarchy, structuring as you go in an omnitriangularly oriented evolution.
1033.54 As we explore the interbonding (valencing) of the evolving structural components, we soon discover that the universal interjointing of systems__and their foldability__permit their angularly hinged convergence into congruence of vertexes (single bonding), vectors (double bonding), faces (triple bonding), and volumetric congruence (quadri-bonding). Each of these multicongruences appears only as one vertex or one edge or one face aspect. The Eulerean topological accounting as presently practiced__innocent of the inherent synergetical hierarchy of intertransformability__accounts each of these multicongruent topological aspects as consisting of only one of such aspects. This misaccounting has prevented the physicists and chemists from conceptual identification of their data with synergetics' disclosure of nature's comprehensively rational, intercoordinate mathematical system.
1033.55 Only the topological analysis of synergetics can account for all the multicongruent__doubled, tripled, fourfolded__topological aspects by accounting for the initial tetravolume inventories of the comprehensive rhombic dodecahedron and vector equilibrium. The comprehensive rhombic dodecahedron has an initial tetravolume of 48; the vector equilibrium has an inherent tetravolume of 20; their respective initial or primitive inventories of vertexes, vectors, and faces are always present__though often imperceptibly so__at all stages in nature's comprehensive convergence transformation.
2 fold: triangle octavalent
3 fold: tetra quadruvalent
4 fold: cube, octa, apparent cubocta, rhom dodeca
5 fold: icosa, penta dodeca
6 fold: actual cubocta in motion when surface squares collapse
7 axes of symmetry, 14 faces of bubbles & cells: 14faces
Carbon C60 buckyball: truncated icosahedron C60
Boron B80 buckyball: truncated rhombic triacontahedron B80
Tetrakaidecahedron: 14 sided polyhedra includes VE, truncated octahedra (space filler) and hexagonal truncated trapezohedron (14 sided soap foam)
http://en.wikipedia.org/wiki/Tetrakaidecahedron
The more regular honeycombs dualise neatly:
* The cubic honeycomb is self-dual.
* That of octahedra and tetrahedra is dual to that of rhombic dodecahedra.
Check: quasicrystal matrix composed of icosa & star tetra, where the icosa contain nuclei of star tetra.
Da Vincis' star tetrahedron & icosahedron: star tet
Jitterbug transformation: from 4 fold VE through 5 fold icosa to 3 fold tetra VV
The nucleated cubocta is a unique 3D system in Vector Equilibrium, where all 24 circumferential vectors (edges) are the same length as the 12 nuclear radiating vectors (rays). The non-nucleated VE is not structurally rigid with rubber joints (unlike the tetra, octa and icosa of 60 degrees) due to the 6 collapsable square faces of 90 degrees, but with polarised kinetic energy applied (compressed, extended or torqued at opposing triangle or square faces) will transform as follows:
Compressing polar triangles inward: spins through an incomplete icosa to an octa.
Extending polar triangles outward: unstable convex-concave tri-prism, which if equatorially compressed (at evertices or invertices) or polarly torqued forms a webbed pin-hinged double tetra hourglass.
Torqueing polar triangles laterally: 2f (nuc) triangle, folds to tetra.
Compressing polar squares inward: star square, folds to 1/2-octa to 1f triangle.
Extending polar squares outward produces stretched cube, which if equatorially compressed or polarly torqued forms a pin-hinged double 1/2-octa hourglass, folds to a single 1/2-octa to 1f triangle.
Torqueing polar squares laterally: incomplete 2f tetra, folds to saddle form or hexagon or 2f (nuc) triangle to tetra.
Jitterbug collapse to tetra: http://www.rwgrayprojects.com/synergetics/s04/figs/f6108.html
Jitterbug collapse to octa:
6 loops circumscribe a spherical VE: 6 loop VE
Relative Volumes at Grunch: http://grunch.net/archives/47
Concentric hierarchy: here
Quintet dodeca: http://www.newciv.org/Synergetic_Geometry/Quintet_Dodeca.JPEG
http://www.newciv.org/Synergetic_Geometry/amoeba.htm
xkcd symmetree
-
Octet truss IVM virtual space frame allows tourists to see ancient artifacts without disturbing them at Java, Indonesia.
Time & Space Perspective
-
On spherical gravity "attraction" & EM radial wave "repulsion" relationships
2 round objects have more surface area than 1, so they are "attracted" to each other, collision reduces total surface area. Energy has no surface area so is independent of gravity, (it 'curves' around bodies due to reflection pressure?) it radiates outwardly in periodic (tidal) waves linearly from sphere center.
circumferential vectors & great circles: icosa edge vectors 30, icosa great circles 31; cubocta edge vectors 24, cubocta great circles 25
1052.21 Isaac Newton discovered the celestial gravitation interrelationship and expressed it in terms of the second power of the relative distance between the different masses as determined by reference to the radius of one of the interattracted masses. The gravitational relationship is also synergetically statable in terms of the second power of relative frequency of volumetric quanta concentrations of the respectively interattracted masses. Newton's gravitational constant is a radially (frequency) measured rate of spherical surface contraction, while Einstein's radiational constant is a radial (frequency) rate of spherical expansion. (See Secs. 960.12, 1009.31 and 1052.44.)
1052.30 Gravitational Constant: Excess of One Great Circle over Edge Vectors in Vector Equilibrium and Icosahedron: Pondering on Einstein's last problem of the Unified Field Theory, in which he sought to identify and explain the mathematical differentiations between electromagnetics and gravity__the two prime attractive forces of Universe__and recalling in that connection the conclusion of synergetics that gravity operates in spherical embracement, not by direct radial vectors, and recalling that electromagnetics follows the high-tension convex surfaces, possibly the great-circle trunk system of railroad tracks (see Secs. 452 and 458); led to pondering, in surprise, over the fact that the vector equilibrium, which identifies the gravitational behaviors, discloses 25 great circles for the vector equilibrium in respect to its 24 external vector edges, and the icosahedron, which identifies the electron behaviors of electromagnetics, discloses 31 great circles in respect to its 30 external vector edges.
1052.31 In each case, there is an excess of one great circle over the edge vectors. Recalling that the circumferential vector edges of the vector equilibrium exactly equal the radial explosive/implosive forces, while the icosahedron's 30 external edges are longer and more powerful than its 30 radial vectors [What 30 radial vectors?? A star icosa has external equilength pentalateral-bond tets, a cubocta has equilength quadrilateral-bond & equilength mono-radial vectors.], yet each has an excess of one great circle, which great circles must have two polar axes of spin, we encounter once more the excess two polar vertexes characterizing all topological systems, and witness the excess of embracingly cohering forces in contradistinction to the explosively disintegrative forces of Universe.
-
A star tetra, a star octa, and a star icosa each contain a nuclear void (empty space tet, octa, icosa) polyhedron surrounded and structured by reg ext tets. A star cubocta does not contain a void nucleus. A star rh dodeca and star non-nucleated cubocta contain void polyhedron nuclei, but lacking full tet surfaces are not structured. Empty stars can be nucleated by structures: star icosa accepts a nuclear star tetra (free spinning? quasicrystal matrix), star cubocta accepts a nuclear star octa (IVM crystal matrix).
-
domed dive mask
I'd like to get this dive mask, great vision underwater for those who are nearsighted (myopic) like me, and lack sufficient visual accomodation for clear dark adapted acuity.
Vortices in dragonfly flight animation:
http://www.news.cornell.edu/releases/March00/APS_Wang.hrs.html
Spiral column foldable origami: spiral
Fish bones, fermented fish vs cooked fish, calcium carbonate in sea water, sleep
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=921452
Fish-bone peptides (FBP) with a high affinity to Ca were isolated using hydroxyapatite affinity chromatography, and FBP II with a high ratio of phosphopeptide was fractionated in the range of molecular weight 5·0–1·0kDa by ultramembrane filtration. In vitro study elucidated that FBP II could inhibit the formation of insoluble Ca salts in neutral pH. In vivo effects of FBP II on Ca bioavailability were further examined in the ovariectomised rat. During the experimental period, Ca retention was increased and loss of bone mineral was decreased by FBP II supplementation in ovariectomised rats. After the low-Ca diet, the FBP II diet, including both normal level of Ca and vitamin D, significantly decreased Ca loss in faeces and increased Ca retention compared with the control diet. The levels of femoral total Ca, bone mineral density, and strength were also significantly increased by the FBP II diet to levels similar to those of the casein phosphopeptide diet group (no difference; P>0·05). In the present study, the results proved the beneficial effects of fish-meal in preventing Ca deficiency due to increased Ca bioavailability by FBP intake
ocean alkalinity & fish
New research reveals the major influence of fish on maintaining the delicate pH balance of our oceans, vital for the health of coral reefs and other marine life.
The discovery, made by a team of scientists from the UK, US and Canada, could help solve a mystery that has puzzled marine chemists for decades. Published 16 January 2009 in Science, the study provides new insights into the marine carbon cycle, which is undergoing rapid change as a result of global CO2 emissions.
Until now, scientists have believed that the oceans' calcium carbonate, which dissolves to make seawater alkaline, came from the external 'skeletons' of microscopic marine plankton. This study estimates that three to 15 per cent of marine calcium carbonate is in fact produced by fish in their intestines and then excreted. This is a conservative estimate and the team believes it has the potential to be three times higher.
Fish are therefore responsible for contributing a major but previously unrecognised portion of the inorganic carbon that maintains the ocean's acidity balance. The researchers predict that future increases in sea temperature and rising CO2 will cause fish to produce even more calcium carbonate.
To reach these results, the team created two independent computer models which for the first time estimated the total mass of fish in the ocean. They found there are between 812 and 2050 million tonnes (between 812 billion and 2050 billion kilos) of bony fish in the ocean. They then used lab research to establish that these fish produce around 110 million tonnes (110 billion kilos) of calcium carbonate per year.
Calcium carbonate is a white, chalky material that helps control the delicate acidity balance, or pH, of sea water. pH balance is vital for the health of marine ecosystems, including coral reefs, and important in controlling how easily the ocean will absorb and buffer future increases in atmospheric CO2.
This calcium carbonate is being produced by bony fish, a group that includes 90% of marine fish species but not sharks or rays. These fish continuously drink seawater to avoid dehydration. This exposes them to an excess of ingested calcium, which they precipitate into calcium carbonate crystals in the gut. The fish then simply excrete these unwanted chalky solids, sometimes called 'gut rocks', in a process that is separate from digestion and production of faeces.
The study reveals that carbonates excreted by fish are chemically quite different from those produced by plankton. This helps explain a phenomenon that has perplexed oceanographers: the sea becomes more alkaline at much shallower depths than expected. The carbonates produced by microscopic plankton should not be responsible for this alkalinity change, because they sink to much deeper depths intact, often becoming locked up in sediments and rocks for millions of years. In contrast, fish excrete more soluble forms of calcium carbonate that are likely to completely dissolve at much shallower depths (e.g. 500 to 1,000 metres).
Lead author Dr Rod Wilson of the University of Exeter (UK) said: "Our most conservative estimates suggest three to 15 per cent of the oceans' carbonates come from fish, but this range could be up to three times higher. We also know that fish carbonates differ considerably from those produced by plankton"
toads, fish, sharks, CaCO3, etc.
reefs
Photic Sneeze
Photic sneeze: vestige of past tropical lagoon diving ancestors? Aqua-photic Respiratory Cycle forage divers, fast dark-adapted sunlight exhalations...
Y DNA Haplogroup T: Salt trade, boiling brine to trade via dugout for inland goods?
coastal transit/trade 30ka
Upper Rift seasonal fishing camp 770ka: carp, acorn, olive pit, raisin, bark
carp fishing with acorn bait & crabbing 770ka at Lake Hula
23ka bedding, salt and freshwater springs at Sea of Galillee
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC409895/
http://www.ncbi.nlm.nih.gov/pubmed/19125919?ordinalpos=1&itool=PPMCLayout.PPMCAppController.PPMCArticlePage.PPMCPubmedRA&linkpos=2
Similarities between Hs & Pt: proteins, DNA, chromosome
http://academic.reed.edu/biology/professors/srenn/pages/teaching/431S05/431S05_readings/431s05_examples/king_wilson_1975(classic).pdf
numeric sequences
There are four fundamental corners in every system, and each must be triangulated: 4 × 3 = 12. Thus there are twelve degrees of freedom, tetrahedrally organized." Amy Edmondson, A Fuller Explanation, Re. R. Buckminster Fuller, vector equilibrium
Relative Volume Table: (tetra volumes) | (cube volumes)
| form | = tv|cv | form | = tv | cv |
| tetra/coupler | = 1 | 1/3 | star octa | = 12 | 4 |
| double tetra | = 2 | 2/3 | star rh dodeca | = 12 | 4 |
| duo-tet cube | = 3 | 1 | cmpd cubocta ext | = 20 | ~7 |
| reg octa | = 4 | 4/3 | reg icosa int | :~18 | ~6 |
| star tetra | = 5 | 5/3 | star icosa ext | = 20 | ~7 |
| rhom dodeca | = 6 | 2 | cubocta int | = 20 | ~7 |
| 2F coupler | = 8 | 8/3 | 2F cube | = 24 | 8 |
Icosa = 18.51 tv +
Vector edge Cube = 8.49 tv =
Icosa + Vector edge Cube = 27 tv -
Vector diagonal Cube = 3 tv (2 small duotets) =
2F lattice Cube = 24 tv (2 big duotets) -
Octa = 4 tv =
Star Icosa ext = 20 tv or
Cubocta = 20 tv + 8 ext tetra =
Star Cubocta Cube = 28 tv + 6 ext sq pyramids =
Cmpd Cubocta = 40 tv - 8 ext tetra =
Superocta = 6 octa & 8 tetra = 32 tv
compound of (1st stellation of) cube & octahedron (not star cubocta)
Cumulation: tet, octa, cube, icosa, dodeca can be cumulated 4 times
CUMULATION
(Cube & tet can't be stellated but both can be cumulated)
tetra, triakis tetra, cube, 12-faced star deltahedron (star tetra)
cube, tetrakis hexahedron, rhomb dodeca, 24 face star deltahedron (star cube)
octa, sm triakis octa, stella octangula/duotet (star octa)
star tetra, star octa (domain net of cubocta), star icosa
Now excluding the nucleic polyhedron volume:
View of surface tets as skeletal structure, equi length struts
Star Tet: nuc tet void, 4 tets, 6 circ + 12 ext struts = 18
Star Octa: nuc octa void, 8 tets, 12 circ + 24 ext struts = 36
Star Icosa: nuc icosa void, 20 tets, 30 circ + 60 ext struts = 90
I think the star tetra, star octa and star icosa qualify as 'VE', if the central polyhedra (reg tet, reg octa, reg icosa) is considered to be the nucleus. All the connecting vectors are same length AFAICT. Eg. the star icosa has all equal length vectors and has no centroid vectors (which would be a different length). So you need to specify which VE:
VE cubocta
VE star tetra
VE star octa
VE star icosa
The star tetra has 12 face planes
Multiplication by division: http://synergeticists.org/synergetics/plates/figs/plate03.html
Noting Kirby's & Alan's relative volume tables here:
math
Eschers solid
A 1F cube has 3 tv. First stellation of a cube is a rhombic dodeca of 6 tv.
First stellation of a rhombic dodeca is Escher's Solid, of 12 tv,
half the volume of the 2F cube, same as the star octa.
The volume of the cuboctahedron is 5/6 of that of the enclosing cube and 5/8 of that of the enclosing octahedron. The cuboctahedron shares its edges and vertex arrangement with two nonconvex uniform polyhedra: the cubohemioctahedron (having the square faces in common) and the octahemioctahedron (having the triangular faces in common).
I suggest adding one more, some star polyhedra with identical regular tetrahedra, the internal central polyhedron is a void*, since the external tetras produce the structure, so no additional struts required:
star tetra: 4 tetras (star tet - tet nucleus)
star octa: 8 tetras (duotet - octa nucleus)
star cubocta: 8 tetras (cube - cubocta nucleus)
=====================
star icosa: 20 tetras (4 + 8 + 8) * jitterbug transformation
*These exclude the nuclear polyhedron, since it is a void built by the exoskeleton of structural tets and overlapped struts are unnecessary.
I haven't checked if the orientation of the 20 tets of the star icosa match with those of the others, or if they need to be rotated or jitterbugged to fit the icosa.
compound cubocta & 120 cell
What can fit into an icosa? a tet. an octa. a star tet? a star octa?
unknown.
rhombic dodeca (cube with pyramidal faces combine coplanar pairs of triangles into rhombi) rhomdodeca from cube+6pyramid (differs from star cube with noncoplanar pairs of triangles)
star rhombic dodeca & star octa:
star vol
C60 Carbon buckyball fullerene: 60 vertices divided into 12 pentagon sets; 32 faces of 12 pentas and 20 hexas, 90 edges of 60 pentagonal edges (single bonds)and 30 hexagonal edges (double bonds), each hexagon has alternating single and double bonds. Dual of truncated icosahedron C60 with 32 faces and 60 vertices is the pentakis dodecahedron (triangulated C60) of 60 faces and 32 vertices.
syn
1033.53 The vector equilibrium jitterbug provides the articulative model for demonstrating the always omnisymmetrical, divergently expanding or convergently contracting intertransformability of the entire primitive polyhedral hierarchy, structuring as you go in an omnitriangularly oriented evolution.
1033.54 As we explore the interbonding (valencing) of the evolving structural components, we soon discover that the universal interjointing of systems__and their foldability__permit their angularly hinged convergence into congruence of vertexes (single bonding), vectors (double bonding), faces (triple bonding), and volumetric congruence (quadri-bonding). Each of these multicongruences appears only as one vertex or one edge or one face aspect. The Eulerean topological accounting as presently practiced__innocent of the inherent synergetical hierarchy of intertransformability__accounts each of these multicongruent topological aspects as consisting of only one of such aspects. This misaccounting has prevented the physicists and chemists from conceptual identification of their data with synergetics' disclosure of nature's comprehensively rational, intercoordinate mathematical system.
1033.55 Only the topological analysis of synergetics can account for all the multicongruent__doubled, tripled, fourfolded__topological aspects by accounting for the initial tetravolume inventories of the comprehensive rhombic dodecahedron and vector equilibrium. The comprehensive rhombic dodecahedron has an initial tetravolume of 48; the vector equilibrium has an inherent tetravolume of 20; their respective initial or primitive inventories of vertexes, vectors, and faces are always present__though often imperceptibly so__at all stages in nature's comprehensive convergence transformation.
2 fold: triangle octavalent
3 fold: tetra quadruvalent
4 fold: cube, octa, apparent cubocta, rhom dodeca
5 fold: icosa, penta dodeca
6 fold: actual cubocta in motion when surface squares collapse
7 axes of symmetry, 14 faces of bubbles & cells: 14faces
Carbon C60 buckyball: truncated icosahedron C60
Boron B80 buckyball: truncated rhombic triacontahedron B80
Tetrakaidecahedron: 14 sided polyhedra includes VE, truncated octahedra (space filler) and hexagonal truncated trapezohedron (14 sided soap foam)
http://en.wikipedia.org/wiki/Tetrakaidecahedron
The more regular honeycombs dualise neatly:
* The cubic honeycomb is self-dual.
* That of octahedra and tetrahedra is dual to that of rhombic dodecahedra.
Check: quasicrystal matrix composed of icosa & star tetra, where the icosa contain nuclei of star tetra.
Da Vincis' star tetrahedron & icosahedron: star tet
Jitterbug transformation: from 4 fold VE through 5 fold icosa to 3 fold tetra VV
The nucleated cubocta is a unique 3D system in Vector Equilibrium, where all 24 circumferential vectors (edges) are the same length as the 12 nuclear radiating vectors (rays). The non-nucleated VE is not structurally rigid with rubber joints (unlike the tetra, octa and icosa of 60 degrees) due to the 6 collapsable square faces of 90 degrees, but with polarised kinetic energy applied (compressed, extended or torqued at opposing triangle or square faces) will transform as follows:
Compressing polar triangles inward: spins through an incomplete icosa to an octa.
Extending polar triangles outward: unstable convex-concave tri-prism, which if equatorially compressed (at evertices or invertices) or polarly torqued forms a webbed pin-hinged double tetra hourglass.
Torqueing polar triangles laterally: 2f (nuc) triangle, folds to tetra.
Compressing polar squares inward: star square, folds to 1/2-octa to 1f triangle.
Extending polar squares outward produces stretched cube, which if equatorially compressed or polarly torqued forms a pin-hinged double 1/2-octa hourglass, folds to a single 1/2-octa to 1f triangle.
Torqueing polar squares laterally: incomplete 2f tetra, folds to saddle form or hexagon or 2f (nuc) triangle to tetra.
Jitterbug collapse to tetra: http://www.rwgrayprojects.com/synergetics/s04/figs/f6108.html
Jitterbug collapse to octa:
6 loops circumscribe a spherical VE: 6 loop VE
Relative Volumes at Grunch: http://grunch.net/archives/47
Concentric hierarchy: here
Quintet dodeca: http://www.newciv.org/Synergetic_Geometry/Quintet_Dodeca.JPEG
http://www.newciv.org/Synergetic_Geometry/amoeba.htm
xkcd symmetree
-
Octet truss IVM virtual space frame allows tourists to see ancient artifacts without disturbing them at Java, Indonesia.
Time & Space Perspective
-
On spherical gravity "attraction" & EM radial wave "repulsion" relationships
2 round objects have more surface area than 1, so they are "attracted" to each other, collision reduces total surface area. Energy has no surface area so is independent of gravity, (it 'curves' around bodies due to reflection pressure?) it radiates outwardly in periodic (tidal) waves linearly from sphere center.
circumferential vectors & great circles: icosa edge vectors 30, icosa great circles 31; cubocta edge vectors 24, cubocta great circles 25
1052.21 Isaac Newton discovered the celestial gravitation interrelationship and expressed it in terms of the second power of the relative distance between the different masses as determined by reference to the radius of one of the interattracted masses. The gravitational relationship is also synergetically statable in terms of the second power of relative frequency of volumetric quanta concentrations of the respectively interattracted masses. Newton's gravitational constant is a radially (frequency) measured rate of spherical surface contraction, while Einstein's radiational constant is a radial (frequency) rate of spherical expansion. (See Secs. 960.12, 1009.31 and 1052.44.)
1052.30 Gravitational Constant: Excess of One Great Circle over Edge Vectors in Vector Equilibrium and Icosahedron: Pondering on Einstein's last problem of the Unified Field Theory, in which he sought to identify and explain the mathematical differentiations between electromagnetics and gravity__the two prime attractive forces of Universe__and recalling in that connection the conclusion of synergetics that gravity operates in spherical embracement, not by direct radial vectors, and recalling that electromagnetics follows the high-tension convex surfaces, possibly the great-circle trunk system of railroad tracks (see Secs. 452 and 458); led to pondering, in surprise, over the fact that the vector equilibrium, which identifies the gravitational behaviors, discloses 25 great circles for the vector equilibrium in respect to its 24 external vector edges, and the icosahedron, which identifies the electron behaviors of electromagnetics, discloses 31 great circles in respect to its 30 external vector edges.
1052.31 In each case, there is an excess of one great circle over the edge vectors. Recalling that the circumferential vector edges of the vector equilibrium exactly equal the radial explosive/implosive forces, while the icosahedron's 30 external edges are longer and more powerful than its 30 radial vectors [What 30 radial vectors?? A star icosa has external equilength pentalateral-bond tets, a cubocta has equilength quadrilateral-bond & equilength mono-radial vectors.], yet each has an excess of one great circle, which great circles must have two polar axes of spin, we encounter once more the excess two polar vertexes characterizing all topological systems, and witness the excess of embracingly cohering forces in contradistinction to the explosively disintegrative forces of Universe.
-
A star tetra, a star octa, and a star icosa each contain a nuclear void (empty space tet, octa, icosa) polyhedron surrounded and structured by reg ext tets. A star cubocta does not contain a void nucleus. A star rh dodeca and star non-nucleated cubocta contain void polyhedron nuclei, but lacking full tet surfaces are not structured. Empty stars can be nucleated by structures: star icosa accepts a nuclear star tetra (free spinning? quasicrystal matrix), star cubocta accepts a nuclear star octa (IVM crystal matrix).
-
domed dive mask
I'd like to get this dive mask, great vision underwater for those who are nearsighted (myopic) like me, and lack sufficient visual accomodation for clear dark adapted acuity.
Vortices in dragonfly flight animation:
http://www.news.cornell.edu/releases/March00/APS_Wang.hrs.html
Spiral column foldable origami: spiral
Fish bones, fermented fish vs cooked fish, calcium carbonate in sea water, sleep
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=921452
Fish-bone peptides (FBP) with a high affinity to Ca were isolated using hydroxyapatite affinity chromatography, and FBP II with a high ratio of phosphopeptide was fractionated in the range of molecular weight 5·0–1·0kDa by ultramembrane filtration. In vitro study elucidated that FBP II could inhibit the formation of insoluble Ca salts in neutral pH. In vivo effects of FBP II on Ca bioavailability were further examined in the ovariectomised rat. During the experimental period, Ca retention was increased and loss of bone mineral was decreased by FBP II supplementation in ovariectomised rats. After the low-Ca diet, the FBP II diet, including both normal level of Ca and vitamin D, significantly decreased Ca loss in faeces and increased Ca retention compared with the control diet. The levels of femoral total Ca, bone mineral density, and strength were also significantly increased by the FBP II diet to levels similar to those of the casein phosphopeptide diet group (no difference; P>0·05). In the present study, the results proved the beneficial effects of fish-meal in preventing Ca deficiency due to increased Ca bioavailability by FBP intake
ocean alkalinity & fish
New research reveals the major influence of fish on maintaining the delicate pH balance of our oceans, vital for the health of coral reefs and other marine life.
The discovery, made by a team of scientists from the UK, US and Canada, could help solve a mystery that has puzzled marine chemists for decades. Published 16 January 2009 in Science, the study provides new insights into the marine carbon cycle, which is undergoing rapid change as a result of global CO2 emissions.
Until now, scientists have believed that the oceans' calcium carbonate, which dissolves to make seawater alkaline, came from the external 'skeletons' of microscopic marine plankton. This study estimates that three to 15 per cent of marine calcium carbonate is in fact produced by fish in their intestines and then excreted. This is a conservative estimate and the team believes it has the potential to be three times higher.
Fish are therefore responsible for contributing a major but previously unrecognised portion of the inorganic carbon that maintains the ocean's acidity balance. The researchers predict that future increases in sea temperature and rising CO2 will cause fish to produce even more calcium carbonate.
To reach these results, the team created two independent computer models which for the first time estimated the total mass of fish in the ocean. They found there are between 812 and 2050 million tonnes (between 812 billion and 2050 billion kilos) of bony fish in the ocean. They then used lab research to establish that these fish produce around 110 million tonnes (110 billion kilos) of calcium carbonate per year.
Calcium carbonate is a white, chalky material that helps control the delicate acidity balance, or pH, of sea water. pH balance is vital for the health of marine ecosystems, including coral reefs, and important in controlling how easily the ocean will absorb and buffer future increases in atmospheric CO2.
This calcium carbonate is being produced by bony fish, a group that includes 90% of marine fish species but not sharks or rays. These fish continuously drink seawater to avoid dehydration. This exposes them to an excess of ingested calcium, which they precipitate into calcium carbonate crystals in the gut. The fish then simply excrete these unwanted chalky solids, sometimes called 'gut rocks', in a process that is separate from digestion and production of faeces.
The study reveals that carbonates excreted by fish are chemically quite different from those produced by plankton. This helps explain a phenomenon that has perplexed oceanographers: the sea becomes more alkaline at much shallower depths than expected. The carbonates produced by microscopic plankton should not be responsible for this alkalinity change, because they sink to much deeper depths intact, often becoming locked up in sediments and rocks for millions of years. In contrast, fish excrete more soluble forms of calcium carbonate that are likely to completely dissolve at much shallower depths (e.g. 500 to 1,000 metres).
Lead author Dr Rod Wilson of the University of Exeter (UK) said: "Our most conservative estimates suggest three to 15 per cent of the oceans' carbonates come from fish, but this range could be up to three times higher. We also know that fish carbonates differ considerably from those produced by plankton"
toads, fish, sharks, CaCO3, etc.
reefs
Photic Sneeze
Photic sneeze: vestige of past tropical lagoon diving ancestors? Aqua-photic Respiratory Cycle forage divers, fast dark-adapted sunlight exhalations...
Y DNA Haplogroup T: Salt trade, boiling brine to trade via dugout for inland goods?
coastal transit/trade 30ka
Upper Rift seasonal fishing camp 770ka: carp, acorn, olive pit, raisin, bark
carp fishing with acorn bait & crabbing 770ka at Lake Hula
23ka bedding, salt and freshwater springs at Sea of Galillee
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC409895/
http://www.ncbi.nlm.nih.gov/pubmed/19125919?ordinalpos=1&itool=PPMCLayout.PPMCAppController.PPMCArticlePage.PPMCPubmedRA&linkpos=2
Similarities between Hs & Pt: proteins, DNA, chromosome
http://academic.reed.edu/biology/professors/srenn/pages/teaching/431S05/431S05_readings/431s05_examples/king_wilson_1975(classic).pdf
numeric sequences
Tuesday, December 22, 2009
197th post: Hey, Its Ant-a Claws !!
South of Spain: Mar Menor Lagoon
Ant-a Claws
-
In honor of Darwins' anniversary of On the Origin of Species.
New Papyrus: Darwin
it takes 20 000 genes to make a nematode and 25 000 to make a human
http://www.livescience.com/technology/technovelgy_eyes_041104.html
Charles Darwin recognized that the eye would be a real test of the theory of evolution. He suggested that it might be possible to evolve an eye from "imperfect and simple" forms:
"To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree.
"Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real."
Scientists today believe that the eye could evolve from a single light-sensing cell. Scientists disagree over whether it evolved just once, or many times.
It turns out that Nature is both creative and generous with her gifts. Recent research has shown that the tiny marine worm Platynereis dumerilii has two types of light-sensing cells. The eyes of the worm have rhabdomeric photoreceptors, a compound lens formation that is seen almost exclusively in insect eyes. Rhabdomeric photoreceptors are covered in little finger-like protrusions. In its brain, however, it has a different kind of light-sensing cells - ciliary cells that are seen in vertebrate animals. Ciliary cells have hair-like cilia that extend outward and branch out like tiny umbrellas. Two different ways of sensing light in a single organism! images
http://scienceblogs.com/pharyngula/2006/09/rhabdomeric_and_ciliary_eyes.php
Researcher Joachim Wittbrodt of the European Molecular Biology Laboratory in Heidelberg, Germany speculates that the ciliary cells may regulate the worm's daily activity cycle, saying "We think they are related to circadian rhythms. We have found that there is a direct connection to the area used for locomotion... In the beginning we had a toolbox... what was in the brain in the worm ends up in our eye." If the animal had two copies of the genes needed to make one kind of photoreceptor, speculates Wittbrodt, then the extra set would have been free to evolve into the other photoreceptor. Different animals would subsequently evolve to use the two options in different ways.
-
Genome: Ramen noodle folding form (no knots) is fractal globule based on icosa-dodecahedron.
"perfect" genome code
empirical genome code
"perfect" periodic table
-
I have speculated earlier here and elsewhere, that the human thumb's missing bone and associated muscle evolutionarily moved to become the fused mandible (lower jaw) and tongue.
-
I posted this comment at a biology website (RDF), in response to why flies have 6 legs and most vertebrates have only 4 [clue - beetles have 4 wings/jaws, reptiles have 4 legs]:
bilateral pentadactyle digits (insect legs/"hands"/wings/"jaws")*
bilateral pentadactyle digits (invertebrate squid tentacles)*
bilateral pentadactyle digits (vertebrate fingers/toes)*
(larval bilateral) pentadactyle digits (starfish or sand dollar)*
icosahedral/pentameric (eg. virus) symmetry (12 oral/anal sets of five cilia)
*digits can be asexually replicated (due to incomplete meiosis?) or mutatively lost, body segments also, so bilateral millipedes simply have axial multiple copies of their earlier rear set, while bilateral vertebrates have axial duplicated the pelvis from the forelimb carriage or axial duplicated the rear limbs on a rear part of the primitive forelimb carriage which eventually moved caudally.
Flies have 6 legs, 2 wings, 2 wing knobs = 10 digits (no jaws just sharp tubes, larval jaws are forelimbs)
Spiders/crabs have 8 legs, 2 pedipalps ("jawclaws") = 10 digits (no wings)
Squid have 8 regular tentacles, 2 long "thumb" tentacles = 10 digits
Reptiles, fish, mammals (primitive) have 10 digits (forelimbs), 10 digits (rear limbs)
Evo-devo, human mandible/tongue associates with the missing thumb bone and muscle, while the maxillae associates with the four fingers (before mandibular separation, all five fingers).
Probably, due to the developmental order, a fly would be more likely born without wing knobs or wings than to be born without legs, since legs seem to be more ancient. One born without a leg pair probably also has other more severe genetic mutations, especially in internal segmental replication. While a reptile with 6 legs must oxygenate them with lungs, sufficient oxygenation is critical (dolphins lost their legs as oxygen conservation became more significant) while small insects' spiracles provide enough O2 for many legs, and wings help gain more O2. Perhaps.
-
There is an invertebrate (marine proto-crustacean?) which cannot eat unless it locomotes all limbs, its jaws can't chew unless its digits are moving. This would seem very primitive, since lobster claws and fish jaws operate independently from the legs or fins. Note that while larval caterpillars chew using their 4 forelegs/jaws, adult butterflies only suck nectar while still.
Caterpillars chew with forelimbs modified into jaws, during pupation these jaws reform into webbed wings, so butterflies can fly but can't chew. Grasshoppers do not pupate, they go through stages of enlargement and add wings at a certain instar stage (they can't eat at this stage). The adult grasshopper can both leap and fly. Humans have webbing between thumb and forefinger and between maxillae and mandible (cheeks), in flying insects the same genes form webbed wings associated with jaws; initially (ancestrally) this webbing assisted in filter feeding in early marine invertebrate, moving food particles closer to the mouth orifice.
The primitive invertebrate ancestor had an oral-GI-anal pore/tube with 5 mobile cilia, with variable degrees of rigidity (tentacle vs tendon/bone) and inter-digital webbing, depending on whether the food drifted by current (river) or was static and required cilia pulsation and attachment.
Interesting news confirms earlier speculations
link
Public release date: 20-Apr-2007
[ Print Article | E-mail Article | Close Window ]
Contact: Anna-Lynn Wegener
wegener@embl.de
49-622-138-7452
European Molecular Biology Laboratory
Researchers discover that the centralised nervous system of
vertebrates is much older than expected
The rise of the central nervous system (CNS) in animal evolution has
puzzled scientists for centuries. Vertebrates, insects and worms
evolved from the same ancestor, but their CNSs are different and were
thought to have evolved only after their lineages had split during
evolution. Researchers from the European Molecular Biology Laboratory
(EMBL) in Heidelberg now reveal that the vertebrate nervous system is
probably much older than expected. The study, which is published in
the current issue of Cell, suggests that the last common ancestor of
vertebrates, insects and worms already had a centralised nervous
system resembling that of vertebrates today.
Many animals have evolved complex nervous systems throughout the
course of evolution, but their architectures can differ substantially
between species. ...all these species descend from a common ancestor
called Urbilateria. If this ancestor already possessed a nervous
system, what it might have looked like and how it gave rise to the
diversity of nervous systems seen in animals today is what Detlev
Arendt and his group study at EMBL. To do so, they investigate the
nervous system of a marine annelid worm called Platynereis dumerilii.
"Platynereis can be considered a living fossil," says Arendt, "it
still lives in the same environment as the last common ancestors used
to and has preserved many ancestral features, including a prototype
invertebrate CNS. Comparing the molecular fingerpint of Platynereis
nerve cells with what is known about vertebrates revealed surprising
similarities.
"Our findings were overwhelming," says Alexandru Denes, who carried
out the research in Arendt's lab. "The molecular anatomy of the
developing CNS turned out to be virtually the same in vertebrates and
Platynereis. Corresponding regions give rise to neuron types with
similar molecular fingerprints and these neurons also go on to form
the same neural structures in annelid worm and vertebrate."...
The findings provide strong evidence for a theory that was first put
forward by zoologist Anton Dohrn in 1875. It states that vertebrate
and annelid CNS are of common descent and vertebrates have turned
themselves upside down throughout the course of evolution.
"This explains perfectly why we find the same centralised CNS on the
backside of vertebrates and the bellyside of Platynereis," Arendt
says. "How the inversion occurred and how other invertebrates have
modified the ancestral CNS throughout evolution are the next exciting
questions for evolutionary biologists."
http://chancenecessity.blogspot.com/2009/02/geoffroys-lobster-and-animal-common.html
-
urbilateria
A similar study involving Platynereis dumerlii comes to much the same conclusion. PZ Meyers has a explanation of this bit of research. This result, that humans are evolutionarily slow has been portrayed as a bit of a surprise, but is something that has been in the works for awhile. For example, as early as 1992 it was known that insulin genes in humans and apes evolved at a slower rate than in monkeys. The phenomena, called the “Hominid-rate-slowdown hypothesis”. was first suggested by Goodman in a 1961 paper entitled “The Role of Immunochemical Differences in the Phyletic Development of Human Behavior” (published in Human Biology) and led to papers being published on the subject up to the present (here and here for example).
http://www.hoxfulmonsters.com/2008/12/living-fossil-platynereis-dumerilii-unraveling-the-first-steps-of-eye-evolution
-
updated from earlier post (Vertebrates are inverted invertebrates).
To continue, with slight clarification, if interested:
See Neil Shubins slideshow, especially page 6 slide 5, to compare Hox gene positions in human and fruit fly.
http://tiktaalik.uchicago.edu/book-tools.html
My earlier explanation of primitive pentadactylity (5 digits) didn't well cover the duplication of reptile/mammal rear limbs from the forelimb carriage, this duplication is actually the same as the duplication of (beetle) 4 wings / 4 jaw mouthparts from the primitive frontal digits.
-
(I've briefed the text)
Dragonflies & damselflies (Odonates) can chew but they can't walk, their 6 legs are for perching and grabbing.
http://theatavism.blogspot.com/2009/11/sunday-spinelessness-damselflies.html
"You can tell a damselfly from a dragonfly thanks to the way they hold their wings - damselflies fold them up over their body when they land (butterfly-like) while dragonflies hold them open (moth-like)..." Interesting, butterflies or moths can walk a bit but can't chew, beetles & grasshoppers can walk and chew but their flight is not so well controlled.
wiki lacewings/netwings/antlions
The insect order Neuroptera, or net-winged insects, includes the lacewings, mantidflies, antlions, and their relatives. The adults of this order possess four membranous wings, with the forewings and hindwings about the same size, and with many veins. They have chewing mouthparts, and undergo complete metamorphosis. Neuropterans are soft-bodied insects with relatively few specialised features. They have large lateral compound eyes, and may or may not also have ocelli. Their mouthparts have strong mandibles suitable for chewing, and lack the various adaptations found in most other endopterygote insect groups.
They have four wings, which are usually similar in size and shape, have a generalised pattern of veins. Some Neuropterans have specialised sense organs in their wings, or have bristles or other structures to link their wings together during flight.[4]
The larvae are specialised predators, with elongated mandibles adapted for piercing and sucking. The larval body form varies between different families, depending on the nature of their prey. In general, however, they have three pairs of thoracic legs, each ending in two claws. The abdomen often has adhesive discs on the last two segments.[4] ...ant lions, which bury themselves completely out of sight and ambush prey from "pits" in the soil. Larvae of some Ithonidae are root feeders, and larvae of Sisyridae are aquatic, and feed on freshwater sponges. A few mantispids are parasites of spider egg sacs.
As in other holometabolic orders, there is a pupal stage, generally enclosed in some form of cocoon composed of silk and soil or other debris. The pupa eventually cuts its way out of the cocoon with its mandibles, and may even move about for a short while before undergoing the moult to the adult form.[4] Adults of many groups are also predatory, but some do not feed, or consume only nectar. They are delicate or cumbersome flyers, the spoon wings have rear wings like birds of paradise. Nemoptera
Nemoptera larvae
http://theatavism.blogspot.com/search/label/sci-blogs
It's a springtail (Collembola) - a member of a group of arthropods closely related to (but distinct from insects). They get their common name from a long forked organ, the furcula, that usually sits folded up under the abdomen. The earliest fossil hexapod, and one of the first terrestrial animals, Rhyniella praecursor, is a springtail...'Gomph's live in Antarctic mainland, springtails importantly make soil. Tail derived from crab/crayfish folded tail?
Orobophana pacifica: They are tiny, live on coral rubble on Cook Islands. Even though they live on land they aren't closely related to the "true" landsnails in the order Stylommatophora. To see the difference you need to look into their eyes. If you click on the image above to get a high resolution version you might just be able to see the eye - it's a black dot just underneath the tentacles ("feelers"). In true landsnails like the ones you find in you garden the eyes sit on the ommatophores, a second set of tentacles which are retractable.
bird feet, talons, webbing
Can you walk and talk and chew gum at the same time ?
The mechanics of being Human: a self-balancing, 28-jointed adaptor-based biped; an electro-chemical reduction plant, integral with segregated stowages of special energy extracts in storage batteries, for subsequent actuation of thousands of hydraulic and pneumatic pumps, with motors attached; 62,000 miles of capillaries.... R. Buckminster Fuller-
Bucky: Dictators never create their own opportunities.
A neat series of articles on human facial expressions (non-verbal communication), especially interesting after having read that human cheeks are merely muscular/fatty webbing connecting the mandible to maxilla like butterfly wings. Makes me wonder about the link of the smile to the crinkling of the eyelids or the tightening of the eyebrows, all these facial muscles which communicate internal feelings instantly which are usually masked by reflexive social gestures. They must have evolved in deep time, and gradually fine tuned in humans, a super-social species.
facing others
Human social traits: anonymous, cooperative, infants
Hrdy sociality hypothesis
Corneal blink reflex: trigeminal nerve senses, facial nerve motors to blink at bright light or loud sound or irritating particle in eye.
Corneal reflex
Accomodation reflex
Pupillary light reflex
-
Pigmentation in desert lizards
white lizards
Pigmentation in humans: Baltic blonde & blue eyes from Gulf stream & grain?
pigment
"There is only one spot on the planet where grains will grow despite sub-arctic sunlight.
It is where the warm waters of the Gulf Stream wash ashore. The Baltic is the only place on earth where ocean currents keep it warm enough to grow grain despite dim sunlight. When the inhabitants of this region switched to grain about 6 KYA, they suddenly got insufficient vitamin D to survive. They had stopped eating mostly meat and fish in a place where sunlight was too dim to produce vitamin D in normally pigmented skin. And so they adapted by retaining into adulthood the infantile trait of extreme paleness. Blonde hair and blue eyes were other infantile traits that were just swept along accidentally."
Why did they shift from hunting/gathering (grain processing sorghum in Mozambique 100ka) to complete absolute dependence on grain? What about their cattle/goats/dogs? Fishing seems to have increased rather than decreased amongst Baltic sea peoples with better boat/net technology. Camouflage is always important, whether for predator, prey or combat, but less for farmers. Clothing in cold? Baltic was warm in winter? Europeans also adapted by retaining the ability to digest lactose in adulthood, obtaining vitamin D from milk.
-
Medieval rural Briton women had wider thicker bones than city women
http://www.guardian.co.uk/science/2009/dec/17/women-yorkshire-archeaology-find
Language evolution
http://schott.blogs.nytimes.com/2009/12/16/q-and-a-the-death-of-languages/
-
Whale fossil 4.5ma in Spain: deposited on seafloor 50m deep, now 80m above ground 24km inland. So 4.5ma Medit was high, or tectonic uplifting or both.
http://www.sciencedaily.com/releases/2009/12/091215101716.htm
Dwarf suction-feeding Australian baleen whale
http://news.bbc.co.uk/2/hi/science/nature/8430402.stm
Ant-a Claws
-
In honor of Darwins' anniversary of On the Origin of Species.
New Papyrus: Darwin
it takes 20 000 genes to make a nematode and 25 000 to make a human
http://www.livescience.com/technology/technovelgy_eyes_041104.html
Charles Darwin recognized that the eye would be a real test of the theory of evolution. He suggested that it might be possible to evolve an eye from "imperfect and simple" forms:
"To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree.
"Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real."
Scientists today believe that the eye could evolve from a single light-sensing cell. Scientists disagree over whether it evolved just once, or many times.
It turns out that Nature is both creative and generous with her gifts. Recent research has shown that the tiny marine worm Platynereis dumerilii has two types of light-sensing cells. The eyes of the worm have rhabdomeric photoreceptors, a compound lens formation that is seen almost exclusively in insect eyes. Rhabdomeric photoreceptors are covered in little finger-like protrusions. In its brain, however, it has a different kind of light-sensing cells - ciliary cells that are seen in vertebrate animals. Ciliary cells have hair-like cilia that extend outward and branch out like tiny umbrellas. Two different ways of sensing light in a single organism! images
http://scienceblogs.com/pharyngula/2006/09/rhabdomeric_and_ciliary_eyes.php
Researcher Joachim Wittbrodt of the European Molecular Biology Laboratory in Heidelberg, Germany speculates that the ciliary cells may regulate the worm's daily activity cycle, saying "We think they are related to circadian rhythms. We have found that there is a direct connection to the area used for locomotion... In the beginning we had a toolbox... what was in the brain in the worm ends up in our eye." If the animal had two copies of the genes needed to make one kind of photoreceptor, speculates Wittbrodt, then the extra set would have been free to evolve into the other photoreceptor. Different animals would subsequently evolve to use the two options in different ways.
-
Genome: Ramen noodle folding form (no knots) is fractal globule based on icosa-dodecahedron.
"perfect" genome code
empirical genome code
"perfect" periodic table
-
I have speculated earlier here and elsewhere, that the human thumb's missing bone and associated muscle evolutionarily moved to become the fused mandible (lower jaw) and tongue.
-
I posted this comment at a biology website (RDF), in response to why flies have 6 legs and most vertebrates have only 4 [clue - beetles have 4 wings/jaws, reptiles have 4 legs]:
bilateral pentadactyle digits (insect legs/"hands"/wings/"jaws")*
bilateral pentadactyle digits (invertebrate squid tentacles)*
bilateral pentadactyle digits (vertebrate fingers/toes)*
(larval bilateral) pentadactyle digits (starfish or sand dollar)*
icosahedral/pentameric (eg. virus) symmetry (12 oral/anal sets of five cilia)
*digits can be asexually replicated (due to incomplete meiosis?) or mutatively lost, body segments also, so bilateral millipedes simply have axial multiple copies of their earlier rear set, while bilateral vertebrates have axial duplicated the pelvis from the forelimb carriage or axial duplicated the rear limbs on a rear part of the primitive forelimb carriage which eventually moved caudally.
Flies have 6 legs, 2 wings, 2 wing knobs = 10 digits (no jaws just sharp tubes, larval jaws are forelimbs)
Spiders/crabs have 8 legs, 2 pedipalps ("jawclaws") = 10 digits (no wings)
Squid have 8 regular tentacles, 2 long "thumb" tentacles = 10 digits
Reptiles, fish, mammals (primitive) have 10 digits (forelimbs), 10 digits (rear limbs)
Evo-devo, human mandible/tongue associates with the missing thumb bone and muscle, while the maxillae associates with the four fingers (before mandibular separation, all five fingers).
Probably, due to the developmental order, a fly would be more likely born without wing knobs or wings than to be born without legs, since legs seem to be more ancient. One born without a leg pair probably also has other more severe genetic mutations, especially in internal segmental replication. While a reptile with 6 legs must oxygenate them with lungs, sufficient oxygenation is critical (dolphins lost their legs as oxygen conservation became more significant) while small insects' spiracles provide enough O2 for many legs, and wings help gain more O2. Perhaps.
-
There is an invertebrate (marine proto-crustacean?) which cannot eat unless it locomotes all limbs, its jaws can't chew unless its digits are moving. This would seem very primitive, since lobster claws and fish jaws operate independently from the legs or fins. Note that while larval caterpillars chew using their 4 forelegs/jaws, adult butterflies only suck nectar while still.
Caterpillars chew with forelimbs modified into jaws, during pupation these jaws reform into webbed wings, so butterflies can fly but can't chew. Grasshoppers do not pupate, they go through stages of enlargement and add wings at a certain instar stage (they can't eat at this stage). The adult grasshopper can both leap and fly. Humans have webbing between thumb and forefinger and between maxillae and mandible (cheeks), in flying insects the same genes form webbed wings associated with jaws; initially (ancestrally) this webbing assisted in filter feeding in early marine invertebrate, moving food particles closer to the mouth orifice.
The primitive invertebrate ancestor had an oral-GI-anal pore/tube with 5 mobile cilia, with variable degrees of rigidity (tentacle vs tendon/bone) and inter-digital webbing, depending on whether the food drifted by current (river) or was static and required cilia pulsation and attachment.
Interesting news confirms earlier speculations
link
Public release date: 20-Apr-2007
[ Print Article | E-mail Article | Close Window ]
Contact: Anna-Lynn Wegener
wegener@embl.de
49-622-138-7452
European Molecular Biology Laboratory
Researchers discover that the centralised nervous system of
vertebrates is much older than expected
The rise of the central nervous system (CNS) in animal evolution has
puzzled scientists for centuries. Vertebrates, insects and worms
evolved from the same ancestor, but their CNSs are different and were
thought to have evolved only after their lineages had split during
evolution. Researchers from the European Molecular Biology Laboratory
(EMBL) in Heidelberg now reveal that the vertebrate nervous system is
probably much older than expected. The study, which is published in
the current issue of Cell, suggests that the last common ancestor of
vertebrates, insects and worms already had a centralised nervous
system resembling that of vertebrates today.
Many animals have evolved complex nervous systems throughout the
course of evolution, but their architectures can differ substantially
between species. ...all these species descend from a common ancestor
called Urbilateria. If this ancestor already possessed a nervous
system, what it might have looked like and how it gave rise to the
diversity of nervous systems seen in animals today is what Detlev
Arendt and his group study at EMBL. To do so, they investigate the
nervous system of a marine annelid worm called Platynereis dumerilii.
"Platynereis can be considered a living fossil," says Arendt, "it
still lives in the same environment as the last common ancestors used
to and has preserved many ancestral features, including a prototype
invertebrate CNS. Comparing the molecular fingerpint of Platynereis
nerve cells with what is known about vertebrates revealed surprising
similarities.
"Our findings were overwhelming," says Alexandru Denes, who carried
out the research in Arendt's lab. "The molecular anatomy of the
developing CNS turned out to be virtually the same in vertebrates and
Platynereis. Corresponding regions give rise to neuron types with
similar molecular fingerprints and these neurons also go on to form
the same neural structures in annelid worm and vertebrate."...
The findings provide strong evidence for a theory that was first put
forward by zoologist Anton Dohrn in 1875. It states that vertebrate
and annelid CNS are of common descent and vertebrates have turned
themselves upside down throughout the course of evolution.
"This explains perfectly why we find the same centralised CNS on the
backside of vertebrates and the bellyside of Platynereis," Arendt
says. "How the inversion occurred and how other invertebrates have
modified the ancestral CNS throughout evolution are the next exciting
questions for evolutionary biologists."
http://chancenecessity.blogspot.com/2009/02/geoffroys-lobster-and-animal-common.html
-
urbilateria
A similar study involving Platynereis dumerlii comes to much the same conclusion. PZ Meyers has a explanation of this bit of research. This result, that humans are evolutionarily slow has been portrayed as a bit of a surprise, but is something that has been in the works for awhile. For example, as early as 1992 it was known that insulin genes in humans and apes evolved at a slower rate than in monkeys. The phenomena, called the “Hominid-rate-slowdown hypothesis”. was first suggested by Goodman in a 1961 paper entitled “The Role of Immunochemical Differences in the Phyletic Development of Human Behavior” (published in Human Biology) and led to papers being published on the subject up to the present (here and here for example).
http://www.hoxfulmonsters.com/2008/12/living-fossil-platynereis-dumerilii-unraveling-the-first-steps-of-eye-evolution
-
updated from earlier post (Vertebrates are inverted invertebrates).
To continue, with slight clarification, if interested:
See Neil Shubins slideshow, especially page 6 slide 5, to compare Hox gene positions in human and fruit fly.
http://tiktaalik.uchicago.edu/book-tools.html
My earlier explanation of primitive pentadactylity (5 digits) didn't well cover the duplication of reptile/mammal rear limbs from the forelimb carriage, this duplication is actually the same as the duplication of (beetle) 4 wings / 4 jaw mouthparts from the primitive frontal digits.
-
(I've briefed the text)
Dragonflies & damselflies (Odonates) can chew but they can't walk, their 6 legs are for perching and grabbing.
http://theatavism.blogspot.com/2009/11/sunday-spinelessness-damselflies.html
"You can tell a damselfly from a dragonfly thanks to the way they hold their wings - damselflies fold them up over their body when they land (butterfly-like) while dragonflies hold them open (moth-like)..." Interesting, butterflies or moths can walk a bit but can't chew, beetles & grasshoppers can walk and chew but their flight is not so well controlled.
wiki lacewings/netwings/antlions
The insect order Neuroptera, or net-winged insects, includes the lacewings, mantidflies, antlions, and their relatives. The adults of this order possess four membranous wings, with the forewings and hindwings about the same size, and with many veins. They have chewing mouthparts, and undergo complete metamorphosis. Neuropterans are soft-bodied insects with relatively few specialised features. They have large lateral compound eyes, and may or may not also have ocelli. Their mouthparts have strong mandibles suitable for chewing, and lack the various adaptations found in most other endopterygote insect groups.
They have four wings, which are usually similar in size and shape, have a generalised pattern of veins. Some Neuropterans have specialised sense organs in their wings, or have bristles or other structures to link their wings together during flight.[4]
The larvae are specialised predators, with elongated mandibles adapted for piercing and sucking. The larval body form varies between different families, depending on the nature of their prey. In general, however, they have three pairs of thoracic legs, each ending in two claws. The abdomen often has adhesive discs on the last two segments.[4] ...ant lions, which bury themselves completely out of sight and ambush prey from "pits" in the soil. Larvae of some Ithonidae are root feeders, and larvae of Sisyridae are aquatic, and feed on freshwater sponges. A few mantispids are parasites of spider egg sacs.
As in other holometabolic orders, there is a pupal stage, generally enclosed in some form of cocoon composed of silk and soil or other debris. The pupa eventually cuts its way out of the cocoon with its mandibles, and may even move about for a short while before undergoing the moult to the adult form.[4] Adults of many groups are also predatory, but some do not feed, or consume only nectar. They are delicate or cumbersome flyers, the spoon wings have rear wings like birds of paradise. Nemoptera
Nemoptera larvae
http://theatavism.blogspot.com/search/label/sci-blogs
It's a springtail (Collembola) - a member of a group of arthropods closely related to (but distinct from insects). They get their common name from a long forked organ, the furcula, that usually sits folded up under the abdomen. The earliest fossil hexapod, and one of the first terrestrial animals, Rhyniella praecursor, is a springtail...'Gomph's live in Antarctic mainland, springtails importantly make soil. Tail derived from crab/crayfish folded tail?
Orobophana pacifica: They are tiny, live on coral rubble on Cook Islands. Even though they live on land they aren't closely related to the "true" landsnails in the order Stylommatophora. To see the difference you need to look into their eyes. If you click on the image above to get a high resolution version you might just be able to see the eye - it's a black dot just underneath the tentacles ("feelers"). In true landsnails like the ones you find in you garden the eyes sit on the ommatophores, a second set of tentacles which are retractable.
bird feet, talons, webbing
Can you walk and talk and chew gum at the same time ?
The mechanics of being Human: a self-balancing, 28-jointed adaptor-based biped; an electro-chemical reduction plant, integral with segregated stowages of special energy extracts in storage batteries, for subsequent actuation of thousands of hydraulic and pneumatic pumps, with motors attached; 62,000 miles of capillaries.... R. Buckminster Fuller-
Bucky: Dictators never create their own opportunities.
A neat series of articles on human facial expressions (non-verbal communication), especially interesting after having read that human cheeks are merely muscular/fatty webbing connecting the mandible to maxilla like butterfly wings. Makes me wonder about the link of the smile to the crinkling of the eyelids or the tightening of the eyebrows, all these facial muscles which communicate internal feelings instantly which are usually masked by reflexive social gestures. They must have evolved in deep time, and gradually fine tuned in humans, a super-social species.
facing others
Human social traits: anonymous, cooperative, infants
Hrdy sociality hypothesis
Corneal blink reflex: trigeminal nerve senses, facial nerve motors to blink at bright light or loud sound or irritating particle in eye.
Corneal reflex
Accomodation reflex
Pupillary light reflex
-
Pigmentation in desert lizards
white lizards
Pigmentation in humans: Baltic blonde & blue eyes from Gulf stream & grain?
pigment
"There is only one spot on the planet where grains will grow despite sub-arctic sunlight.
It is where the warm waters of the Gulf Stream wash ashore. The Baltic is the only place on earth where ocean currents keep it warm enough to grow grain despite dim sunlight. When the inhabitants of this region switched to grain about 6 KYA, they suddenly got insufficient vitamin D to survive. They had stopped eating mostly meat and fish in a place where sunlight was too dim to produce vitamin D in normally pigmented skin. And so they adapted by retaining into adulthood the infantile trait of extreme paleness. Blonde hair and blue eyes were other infantile traits that were just swept along accidentally."
Why did they shift from hunting/gathering (grain processing sorghum in Mozambique 100ka) to complete absolute dependence on grain? What about their cattle/goats/dogs? Fishing seems to have increased rather than decreased amongst Baltic sea peoples with better boat/net technology. Camouflage is always important, whether for predator, prey or combat, but less for farmers. Clothing in cold? Baltic was warm in winter? Europeans also adapted by retaining the ability to digest lactose in adulthood, obtaining vitamin D from milk.
-
Medieval rural Briton women had wider thicker bones than city women
http://www.guardian.co.uk/science/2009/dec/17/women-yorkshire-archeaology-find
Language evolution
http://schott.blogs.nytimes.com/2009/12/16/q-and-a-the-death-of-languages/
-
Whale fossil 4.5ma in Spain: deposited on seafloor 50m deep, now 80m above ground 24km inland. So 4.5ma Medit was high, or tectonic uplifting or both.
http://www.sciencedaily.com/releases/2009/12/091215101716.htm
Dwarf suction-feeding Australian baleen whale
http://news.bbc.co.uk/2/hi/science/nature/8430402.stm
Tuesday, November 24, 2009
Relative volumes & concentric hierarchy
tetra tripod table, balloonage
Icosa alloys mimic elements:
Icosa
http://www.sciencedaily.com/releases/2005/02/050205125336.htm
http://www.sciencedaily.com/releases/2009/12/091228152348.htm
Sphere/tet/cube packing, entropy, tets in quasicrystal disks, density in box container
quasi-crystal tet packing
Researchers packed tetrahedra into a cubic box more densely than ever before: 85.03
(Cubes have a 100 percent packing fraction in a cubic box, while spheres pack at only 74 percent.) The tetrahedron was for decades conjectured to be the only solid that packs less densely than spheres, until just last year when U-M mathematics graduate student Elizabeth Chen found an arrangement of 77% that proved that speculation wrong.
the more significant finding is that the tetrahedrons can unexpectedly organize into intricate quasicrystals at a point in the computer simulation when they take up roughly half the space in the theoretical box.
In this computer experiment, many thousands of tetrahedrons organized into dodecagonal, or 12-fold, quasicrystals made of parallel stacks of rings around pentagonal dipyramids. A pentagonal dipyramid contains five tetrahedrons arranged into a disk. The researchers discovered that this motif plays a key role in the overall packing. In the simulation, the tetrahedrons organized into a quasicrystal and settled on a packing that, when compressed further, used up 83 percent of the space. Engel then reorganized the shapes into a "quasicrystalline approximate," which is a periodic crystal closely resembling the quasicrystal. He found an arrangement that filled more than 85 percent of the space.
This is the first result showing such a complicated self-arrangement of hard particles without help from attractive interactions such as chemical bonds, Glotzer said.
Thermos vacuum allows IR radiation outwards through glass, photonic crystals reduce IR heat loss better than pure vacuum
In a typical thermos, a vacuum is used to reduce heat transfer. Scientists have found that layers of photonic crystals in a vacuum can reduce the thermal conductance to about half that of a pure vacuum. Basically, heat can be transferred from one material to another in three main ways: convection, conduction, and radiation. Conduction and convection both require some kind of material medium for heat to pass through; therefore, the lack of material in a pure vacuum greatly minimizes the effectiveness of these two processes. However, heat can also be transferred through infrared radiation, a form of light that is invisible but can be felt as heat. In the example of the thermos, infrared radiation can travel through the vacuum to the thermos' outer wall; when absorbed by the outer wall, the radiation causes the molecules in the outer wall to vibrate and release heat. Significantly, photonic crystals can have band gaps that forbid propagation of certain frequency ranges of light. In this case, they could be used to block infrared radiation.
The scientists found that a 100-micron-thick structure made of a stack of 10 photonic crystal layers, each 1 μm thick and separated by 90-μm gaps of vacuum, could reduce the thermal conductance to about half that of a pure vacuum. In a more recent study, Fan and his colleagues calculated the fraction of all frequencies that the photonic crystal allows through. They were somewhat surprised to find that the thermal conductance doesn't depend on the thickness of the layers but only on how fast light travels through the material, or its index of refraction.
Circles & spheres, flakes and crystals, water & ice
NYTimes
link
super cold
water-tet
Take a regular tetrahedron and set the distance from vertex to tet center as unit 1. Then an
edge of the tet is 1.632993.. . So this number is directly related to the ubiquitous Maraldi angle, 109.47.. degrees (the caltrop angle -- the vertex-center-vertex angle in a regular tet).
CircumsphereRadius/Edge = (1/4)*SQRT(6)
Edge/CircumsphereRadius = 4/SQRT(6)
Vertex-Vertex central Maraldi Angle = arc cos -1/3 ( or ) 2*ACOS(SQRT(1/3))
Giacomo_F._Maraldi: "In math known for obtaining experimentally the angle in the
rhombic dodecahedron shape in 1712, which is still called Maraldi angle."
"Water is a network-forming matter. You can imagine the structure of the network as a kitchen sponge, Matsumoto continues. The sponge structure is originally a kind of foam but membranes are lost, and only the beams - bonds - remain. In both network of water and kitchen sponge, four bonds meet at a point, or node, to form a three dimensionally connected random network. As Plateau pointed out in 19th century, four beams of a foam crosses at a node with regular tetrahedral angle - Maraldi's angle - similar to the waters hydrogen bond network. Matsumoto used computer simulation to look at three ways to change the volume of the foam cells: extension of the bonds, a change in the containing angle between the bonds, and a change in network topology. By discriminating the three contributions, the mechanism became very clear. One contributes to thermal expansion, another one contributes to thermal contraction, and the last one does not. Density maximum is a result of these competing contributions, he explains. "
Caltrops: reg tet 'land mines' The simple design paradigm says that the most elegant, efficient, iconic inventions are necessarily the simplest; like the elastic band, the brick, and the pizza. A caltrop is a simple piece of shaped metal (concrete tank killers); a spiky tetrahedron which, when liberally scattered on the ground, causes a great deal of annoyance to any passing dudes or ponies. And the brilliant thing is that however you drop them, they always land spiky point up.
Biological size, volume, area, fluid flow
size & form
Interaction on Bucky Fuller's tetrahedra as unit volume in synergetic sequence, with input from Allan, Kirby, myself:
Shape: Volume (notes)
MITE: 1/8 (AAB mods)
Tetra: 1 (24 A mods)
Coupler: 1 (8 MITE's)
Stella Octangula: 1.5 (Little octahedron of .5 volume + little tets totalling volume of 1. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Cubocta: 2.5 (1/2 ƒ)
Octa: 4 (dual of cube)
Cube: 3 (dual of octa)
Cube-Octahedron Compound: 4.5 (first stellation of cub-octahedron)*
Rh-Dodeca: 6 (12 half-couplers, other ways)
Escher's Solid: 12 tetras (or 12 couplers [see above], other ways. Notice that the Escher's Solid occupies half the volume of its enclosing cube.)
Cubocta: 20 (volume = 8*2.5)
Cube: 24 (2ƒ)
Stella Octangula: 12 (Octa volume of 4 + 8 tets. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Octahedron: 32 (2ƒ)
Cube-Octahedron Compound: 36 (larger version)
*The (small) cube-octahedron compound has a volume of 4.5, since the cube corners are
half the heights of the regular tetrahedrons.
Relative Volume Sequence: (mine, preliminary, w/ response from Allan)
tet 1 (reg or irreg)
reg tet volume, of course!
coupler 1 (irreg octa)
tet duo 2 (vertex/edge/face bonded)
two tetrahedrons
duotet cube 3
The volume of the cube is 3 tetrahedrons.
octa 4
The volume of the octahedron is 4 tetrahedrons.
The volume of the cube-octahedron compound or first stellation of cub-octahedron is 4.5 tetrahedra. If the octants are elevated even more to regular tetrahedra, then you will get the cuboctahedral star with a volume of 5. (see below)
star tet 5 [tetra-star]
The star tetrahedron is the unfolded net of the pentachoron, which is bounded by 5 tetrahedra.
rhombic triacontahedron 5
reg tet stell cubocta 5 [cubocta star w/ reg tet ecto]
rh dodeca 6
Rhombic dodecahedron has twice the volume of the cube. The volume of the stellated rhombic dodecahedron is 12, which is half the volume of the enclosing 2ƒ cube of volume 24. (below)
star octa 12 [octa star]
Stellated octahedron has half the volume of the enclosing 2ƒ cube of volume 24.
stellated rh dodeca 12
icosa int 18.51 endo
If you think that the icosahedron has volume 20, then you're obviously from another (fourth) dimension! The icosahedron, as we know in our flat Euclidean three-dimensional realm, has a endo- volume of about 18.51 tetrahedra.
cubocta 20 endo
This is the jitterbug, fully extended.
star icosa ext 20 [icosa star reg tet ecto]
But that's assuming that each face has a REGULAR tetrahedron on it.
star cubocta 40 [cubocta star reg tet endo ecto]
The 2ƒ version of the cube-octahedron compound or stellated cuboctahedron has a volume of 36 tetrahedra. For the star cuboctahedron to have a volume of 40, each face would have to be stellated with equilateral triangles (i.e. half-octahedra and regular tetrahedra). (see above)
-
> Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> Its endo-volume of approximately 18.51 does not fit rationally into
> the cosmic hierarchy with whole numbers nor click-stop when
> jitterbugging.
> I found this interesting, a clue perhaps re. 18.51 1/electron
> "The icosahedron contracts to a radius less than the radii of the
> vector equilibrium from which it derived. There is a sphere that is
> tangent to the other 12 spheres at the center of an icosahedron, but
> that sphere is inherently smaller. Its radius is less than the
> spheres in tangency which generate the 12 vertexes of the vector
> equilibrium or icosahedron. Since it is no longer the same-size
> sphere, it is not in the same frequency or in the same energetic
> dimensioning. The two structures are so intimate, but they do not
> have the same amount of energy. For instance, in relation to the
> tetrahedron as unity, the [endo]volume of the icosahedron is 18.51 in
> respect to the vector equilibrium's [endo]volume of 20 [and also the
> star icosa's ectovolume of 20]. The ratio is tantalizing because the
> mass of the electron in respect to the mass of the neutron is one
> over 18.51. That there should be such an important kind of seemingly
> irrational number provides a strong contrast to all the other
> rational data of the tetrahedron as unity, the octahedron as four,
> the vector equilibrium as 20, and the rhombic dodecahedron as six:
> beautiful whole rational numbers". Syn 400.00 system
> "When the volume of a tetrahedron is specified as one unit, other
> ordered polyhedra are found to have precise whole-number volume
> ratios, as opposed to the cumbersome and often irrational quantities
> generated by employing the cube as the unit of volume. Furthermore,
> the tetrahedron has the most surface area per unit of volume".
> (sphere has least) A Fuller Explanation
> http://www.grunch.net/synergetics/ivm.html
> shows IVM in a tet
> from previous:
> Relative volumes: (endo = interior, ecto = exterior shell)
> Tet: (@IVM), vol 1
> Oct: (@IVM), vol 4
> Star Tet: center tet endovol 1 + ectovol 4 (ext tets), vol 5
> Star Oct: center oct endovol 4 + ectovol 8 (@IVM), vol 12
> Star Icosa: center icosa endovol 18.51 + ectovol 20, vol 38.51
> Star Cubocta: endovol 20 + ectovol 20, vol 40
> DD
> On Nov 23, 2009, at 8:00 AM, rybo6 wrote:
> > "Topologically, lines are composed of points."
> > I don't know how it is defined elsewhere, but to me, a line is a
> > point with depth (not = zero), and a point is a line with depth = 0.
> > [Where 'depth' is any direction.] This does not conflict with the
> > definition of a point being a line crossing (which is the same as 2
> > or more vectors meeting at a vertex).
> > The irreg tets that make an icosa, do their struts meet at the
> > center, or do each reach to the opposite face? I thought each face
> > triangle had a tet apex at the icosa center (not modelable with
> > toothpicks), but maybe it goes to the opposite side at a point. Or
> > are there no irreg tets in an icosa?
> > Here (@ link bottom) see the regular icosa and star icosa:
> > http://en.wikipedia.org/wiki/Small_triambic_icosahedron
> > Here see that 2 halves of duotet = cubocta & 2 halves of cubocta =
> > duotet. Do the relative volumes equate?
> > http://groups.yahoo.com/group/synergeo/attachments/folder/1932305706/item/652172707/view
> > http://www.rwgrayprojects.com/synergetics/s09/figs/f5031.html
> > http://www.rwgrayprojects.com/synergetics/s10/figs/f0632.html
> > Relative volumes: (endo = interior, ecto = exterior)
> > Tet: vol 1 (@IVM)
> > Oct: vol 4 (@IVM)
> > Star Tet: center tet endovol 1 + ectovol 4 (ext tets)
> > Star Oct: center oct endovol 4 + ectovol 8 (@IVM)
> > Star Icosa: center icosa endovol 18.51 + ectovol 20
> > Star Cubocta: endovol 20 + ectovol 20
> > Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> > Its endo-volume of approximately 18.51 does not fit rationally into
> > the cosmic hierarchy with whole numbers nor click-stop when
> > jitterbugging. The icosahedron is a phase in between octahedron and
> > vector equilibrium, rather than a definitive stopping point in the
> > flow. The icosahedron is thus restricted to single-layer
> > construction, able to contract/collapse to rigidity, its radius too
> > small to permit having same-size nuclear sphere. (461.05)
> > You could not have two adjacent layers of vector equilibria and then
> > have them collapse to become the icosahedron, it has to be an outside
> > layer, remote from other layers... . It may have as high a frequency
> > as nature may require. The center is vacant. (456.20-1).
> > If the center of an icosa is vacant, should its structural volume be
> > zero? Consider the volume of a donut/torus, is the donut hole volume
> > included in the donut's volume? The donut hole does not contribute to
> > the structure of the donut, it is vacant, but it is part of the donut
> > definition. That is sort of what I think the inner volume of an icosa
> > is, a sort of donut hole, a vestige, therefore not a whole number,
> > perhaps like the interstitial spaces in ball packing.
> > DD
Cubocta = cube & octahedron dual intercept, VE when complete
Octet = octahedron & tetrahedron 3D lattice (CCP), cubocta or star oct IVM
Cuboctet = IVM with cubocta voids (vector flexor) expand-contract jitterbug
shrinks from 20 tetvol hollow cubocta with single bonds to 4 tetvol octet with double bonds
Relativity on earth
Bucky's design science goal was "To make the world work for 100% of humanity in the shortest possible time through spontaneous cooperation without ecological offense or the disadvantage of anyone." Tim Tyler: How can you tell if the world is 'working' for someone? What % of humanity is the world 'working' for today? It seems rather unrealistic to expect nobody to be disadvantaged. Advantages in nature are relative - "evolution is driven by relative fitnesses, not absolute fitnesses. Santayana's aphorism, ``It is not enough to succeed; others must fail.''
At any time, an organism's chances of surviving depend not on how fit it is, but on how fit it is relative to its competition."
http://www.swintons.net/deodands/archives/cat_neutron_teaspoon.html
Neutron stars do really exist. Long after the protons and electrons have long given up the struggle to maintain their identity against the force of gravity, all that is left is neutrons, pressed together into one big atomic nucleus a few kilometres across.
Stars are big balls of gases. Their size is determined by the balance between two opposing forces: gravity pulling the gas inwards, and pressure pushing it outwards. Just like the pressure of air in a balloon, pressure reflects the fact that it's hard to push things together. The pressure depends on how many things you're trying to push together (density), but it also depends on how hard they are to push together. At higher temperatures, the air molecules have more energy, so it takes more effort to keep them from bouncing off each other. There's a relation, then, between the amount of matter and the pressure it exerts in a given setting, which is called the equation of state. We have a fairly good idea of this relationship for the interior of stars like our own sun. Eventually, as our sun radiates energy away, the internal pressure will fall and the gravitational force will increase the density until the point at which electrons are forced together (or, more precisely into degenerate states) forming a white dwarf, and for these conditions we also have a fairly good idea of the equation of state. But for more massive stars, the collapse keeps going past this point and is only halted when the remaining neutrons are forced too 'close' together. And at this point we reach some uncertainty (at least according to 1980 era graduate texts) in what the equation of state is. So there is some real scientific uncertainty in the mass of the neutron teaspoon.
Icosa alloys mimic elements:
Icosa
http://www.sciencedaily.com/releases/2005/02/050205125336.htm
http://www.sciencedaily.com/releases/2009/12/091228152348.htm
Sphere/tet/cube packing, entropy, tets in quasicrystal disks, density in box container
quasi-crystal tet packing
Researchers packed tetrahedra into a cubic box more densely than ever before: 85.03
(Cubes have a 100 percent packing fraction in a cubic box, while spheres pack at only 74 percent.) The tetrahedron was for decades conjectured to be the only solid that packs less densely than spheres, until just last year when U-M mathematics graduate student Elizabeth Chen found an arrangement of 77% that proved that speculation wrong.
the more significant finding is that the tetrahedrons can unexpectedly organize into intricate quasicrystals at a point in the computer simulation when they take up roughly half the space in the theoretical box.
In this computer experiment, many thousands of tetrahedrons organized into dodecagonal, or 12-fold, quasicrystals made of parallel stacks of rings around pentagonal dipyramids. A pentagonal dipyramid contains five tetrahedrons arranged into a disk. The researchers discovered that this motif plays a key role in the overall packing. In the simulation, the tetrahedrons organized into a quasicrystal and settled on a packing that, when compressed further, used up 83 percent of the space. Engel then reorganized the shapes into a "quasicrystalline approximate," which is a periodic crystal closely resembling the quasicrystal. He found an arrangement that filled more than 85 percent of the space.
This is the first result showing such a complicated self-arrangement of hard particles without help from attractive interactions such as chemical bonds, Glotzer said.
Thermos vacuum allows IR radiation outwards through glass, photonic crystals reduce IR heat loss better than pure vacuum
In a typical thermos, a vacuum is used to reduce heat transfer. Scientists have found that layers of photonic crystals in a vacuum can reduce the thermal conductance to about half that of a pure vacuum. Basically, heat can be transferred from one material to another in three main ways: convection, conduction, and radiation. Conduction and convection both require some kind of material medium for heat to pass through; therefore, the lack of material in a pure vacuum greatly minimizes the effectiveness of these two processes. However, heat can also be transferred through infrared radiation, a form of light that is invisible but can be felt as heat. In the example of the thermos, infrared radiation can travel through the vacuum to the thermos' outer wall; when absorbed by the outer wall, the radiation causes the molecules in the outer wall to vibrate and release heat. Significantly, photonic crystals can have band gaps that forbid propagation of certain frequency ranges of light. In this case, they could be used to block infrared radiation.
The scientists found that a 100-micron-thick structure made of a stack of 10 photonic crystal layers, each 1 μm thick and separated by 90-μm gaps of vacuum, could reduce the thermal conductance to about half that of a pure vacuum. In a more recent study, Fan and his colleagues calculated the fraction of all frequencies that the photonic crystal allows through. They were somewhat surprised to find that the thermal conductance doesn't depend on the thickness of the layers but only on how fast light travels through the material, or its index of refraction.
Circles & spheres, flakes and crystals, water & ice
NYTimes
link
super cold
water-tet
Take a regular tetrahedron and set the distance from vertex to tet center as unit 1. Then an
edge of the tet is 1.632993.. . So this number is directly related to the ubiquitous Maraldi angle, 109.47.. degrees (the caltrop angle -- the vertex-center-vertex angle in a regular tet).
CircumsphereRadius/Edge = (1/4)*SQRT(6)
Edge/CircumsphereRadius = 4/SQRT(6)
Vertex-Vertex central Maraldi Angle = arc cos -1/3 ( or ) 2*ACOS(SQRT(1/3))
Giacomo_F._Maraldi: "In math known for obtaining experimentally the angle in the
rhombic dodecahedron shape in 1712, which is still called Maraldi angle."
"Water is a network-forming matter. You can imagine the structure of the network as a kitchen sponge, Matsumoto continues. The sponge structure is originally a kind of foam but membranes are lost, and only the beams - bonds - remain. In both network of water and kitchen sponge, four bonds meet at a point, or node, to form a three dimensionally connected random network. As Plateau pointed out in 19th century, four beams of a foam crosses at a node with regular tetrahedral angle - Maraldi's angle - similar to the waters hydrogen bond network. Matsumoto used computer simulation to look at three ways to change the volume of the foam cells: extension of the bonds, a change in the containing angle between the bonds, and a change in network topology. By discriminating the three contributions, the mechanism became very clear. One contributes to thermal expansion, another one contributes to thermal contraction, and the last one does not. Density maximum is a result of these competing contributions, he explains. "
Caltrops: reg tet 'land mines' The simple design paradigm says that the most elegant, efficient, iconic inventions are necessarily the simplest; like the elastic band, the brick, and the pizza. A caltrop is a simple piece of shaped metal (concrete tank killers); a spiky tetrahedron which, when liberally scattered on the ground, causes a great deal of annoyance to any passing dudes or ponies. And the brilliant thing is that however you drop them, they always land spiky point up.
Biological size, volume, area, fluid flow
size & form
Interaction on Bucky Fuller's tetrahedra as unit volume in synergetic sequence, with input from Allan, Kirby, myself:
Shape: Volume (notes)
MITE: 1/8 (AAB mods)
Tetra: 1 (24 A mods)
Coupler: 1 (8 MITE's)
Stella Octangula: 1.5 (Little octahedron of .5 volume + little tets totalling volume of 1. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Cubocta: 2.5 (1/2 ƒ)
Octa: 4 (dual of cube)
Cube: 3 (dual of octa)
Cube-Octahedron Compound: 4.5 (first stellation of cub-octahedron)*
Rh-Dodeca: 6 (12 half-couplers, other ways)
Escher's Solid: 12 tetras (or 12 couplers [see above], other ways. Notice that the Escher's Solid occupies half the volume of its enclosing cube.)
Cubocta: 20 (volume = 8*2.5)
Cube: 24 (2ƒ)
Stella Octangula: 12 (Octa volume of 4 + 8 tets. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Octahedron: 32 (2ƒ)
Cube-Octahedron Compound: 36 (larger version)
*The (small) cube-octahedron compound has a volume of 4.5, since the cube corners are
half the heights of the regular tetrahedrons.
Relative Volume Sequence: (mine, preliminary, w/ response from Allan)
tet 1 (reg or irreg)
reg tet volume, of course!
coupler 1 (irreg octa)
tet duo 2 (vertex/edge/face bonded)
two tetrahedrons
duotet cube 3
The volume of the cube is 3 tetrahedrons.
octa 4
The volume of the octahedron is 4 tetrahedrons.
The volume of the cube-octahedron compound or first stellation of cub-octahedron is 4.5 tetrahedra. If the octants are elevated even more to regular tetrahedra, then you will get the cuboctahedral star with a volume of 5. (see below)
star tet 5 [tetra-star]
The star tetrahedron is the unfolded net of the pentachoron, which is bounded by 5 tetrahedra.
rhombic triacontahedron 5
reg tet stell cubocta 5 [cubocta star w/ reg tet ecto]
rh dodeca 6
Rhombic dodecahedron has twice the volume of the cube. The volume of the stellated rhombic dodecahedron is 12, which is half the volume of the enclosing 2ƒ cube of volume 24. (below)
star octa 12 [octa star]
Stellated octahedron has half the volume of the enclosing 2ƒ cube of volume 24.
stellated rh dodeca 12
icosa int 18.51 endo
If you think that the icosahedron has volume 20, then you're obviously from another (fourth) dimension! The icosahedron, as we know in our flat Euclidean three-dimensional realm, has a endo- volume of about 18.51 tetrahedra.
cubocta 20 endo
This is the jitterbug, fully extended.
star icosa ext 20 [icosa star reg tet ecto]
But that's assuming that each face has a REGULAR tetrahedron on it.
star cubocta 40 [cubocta star reg tet endo ecto]
The 2ƒ version of the cube-octahedron compound or stellated cuboctahedron has a volume of 36 tetrahedra. For the star cuboctahedron to have a volume of 40, each face would have to be stellated with equilateral triangles (i.e. half-octahedra and regular tetrahedra). (see above)
-
> Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> Its endo-volume of approximately 18.51 does not fit rationally into
> the cosmic hierarchy with whole numbers nor click-stop when
> jitterbugging.
> I found this interesting, a clue perhaps re. 18.51 1/electron
> "The icosahedron contracts to a radius less than the radii of the
> vector equilibrium from which it derived. There is a sphere that is
> tangent to the other 12 spheres at the center of an icosahedron, but
> that sphere is inherently smaller. Its radius is less than the
> spheres in tangency which generate the 12 vertexes of the vector
> equilibrium or icosahedron. Since it is no longer the same-size
> sphere, it is not in the same frequency or in the same energetic
> dimensioning. The two structures are so intimate, but they do not
> have the same amount of energy. For instance, in relation to the
> tetrahedron as unity, the [endo]volume of the icosahedron is 18.51 in
> respect to the vector equilibrium's [endo]volume of 20 [and also the
> star icosa's ectovolume of 20]. The ratio is tantalizing because the
> mass of the electron in respect to the mass of the neutron is one
> over 18.51. That there should be such an important kind of seemingly
> irrational number provides a strong contrast to all the other
> rational data of the tetrahedron as unity, the octahedron as four,
> the vector equilibrium as 20, and the rhombic dodecahedron as six:
> beautiful whole rational numbers". Syn 400.00 system
> "When the volume of a tetrahedron is specified as one unit, other
> ordered polyhedra are found to have precise whole-number volume
> ratios, as opposed to the cumbersome and often irrational quantities
> generated by employing the cube as the unit of volume. Furthermore,
> the tetrahedron has the most surface area per unit of volume".
> (sphere has least) A Fuller Explanation
> http://www.grunch.net/synergetics/ivm.html
> shows IVM in a tet
> from previous:
> Relative volumes: (endo = interior, ecto = exterior shell)
> Tet: (@IVM), vol 1
> Oct: (@IVM), vol 4
> Star Tet: center tet endovol 1 + ectovol 4 (ext tets), vol 5
> Star Oct: center oct endovol 4 + ectovol 8 (@IVM), vol 12
> Star Icosa: center icosa endovol 18.51 + ectovol 20, vol 38.51
> Star Cubocta: endovol 20 + ectovol 20, vol 40
> DD
> On Nov 23, 2009, at 8:00 AM, rybo6 wrote:
> > "Topologically, lines are composed of points."
> > I don't know how it is defined elsewhere, but to me, a line is a
> > point with depth (not = zero), and a point is a line with depth = 0.
> > [Where 'depth' is any direction.] This does not conflict with the
> > definition of a point being a line crossing (which is the same as 2
> > or more vectors meeting at a vertex).
> > The irreg tets that make an icosa, do their struts meet at the
> > center, or do each reach to the opposite face? I thought each face
> > triangle had a tet apex at the icosa center (not modelable with
> > toothpicks), but maybe it goes to the opposite side at a point. Or
> > are there no irreg tets in an icosa?
> > Here (@ link bottom) see the regular icosa and star icosa:
> > http://en.wikipedia.org/wiki/Small_triambic_icosahedron
> > Here see that 2 halves of duotet = cubocta & 2 halves of cubocta =
> > duotet. Do the relative volumes equate?
> > http://groups.yahoo.com/group/synergeo/attachments/folder/1932305706/item/652172707/view
> > http://www.rwgrayprojects.com/synergetics/s09/figs/f5031.html
> > http://www.rwgrayprojects.com/synergetics/s10/figs/f0632.html
> > Relative volumes: (endo = interior, ecto = exterior)
> > Tet: vol 1 (@IVM)
> > Oct: vol 4 (@IVM)
> > Star Tet: center tet endovol 1 + ectovol 4 (ext tets)
> > Star Oct: center oct endovol 4 + ectovol 8 (@IVM)
> > Star Icosa: center icosa endovol 18.51 + ectovol 20
> > Star Cubocta: endovol 20 + ectovol 20
> > Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> > Its endo-volume of approximately 18.51 does not fit rationally into
> > the cosmic hierarchy with whole numbers nor click-stop when
> > jitterbugging. The icosahedron is a phase in between octahedron and
> > vector equilibrium, rather than a definitive stopping point in the
> > flow. The icosahedron is thus restricted to single-layer
> > construction, able to contract/collapse to rigidity, its radius too
> > small to permit having same-size nuclear sphere. (461.05)
> > You could not have two adjacent layers of vector equilibria and then
> > have them collapse to become the icosahedron, it has to be an outside
> > layer, remote from other layers... . It may have as high a frequency
> > as nature may require. The center is vacant. (456.20-1).
> > If the center of an icosa is vacant, should its structural volume be
> > zero? Consider the volume of a donut/torus, is the donut hole volume
> > included in the donut's volume? The donut hole does not contribute to
> > the structure of the donut, it is vacant, but it is part of the donut
> > definition. That is sort of what I think the inner volume of an icosa
> > is, a sort of donut hole, a vestige, therefore not a whole number,
> > perhaps like the interstitial spaces in ball packing.
> > DD
Cubocta = cube & octahedron dual intercept, VE when complete
Octet = octahedron & tetrahedron 3D lattice (CCP), cubocta or star oct IVM
Cuboctet = IVM with cubocta voids (vector flexor) expand-contract jitterbug
shrinks from 20 tetvol hollow cubocta with single bonds to 4 tetvol octet with double bonds
Relativity on earth
Bucky's design science goal was "To make the world work for 100% of humanity in the shortest possible time through spontaneous cooperation without ecological offense or the disadvantage of anyone." Tim Tyler: How can you tell if the world is 'working' for someone? What % of humanity is the world 'working' for today? It seems rather unrealistic to expect nobody to be disadvantaged. Advantages in nature are relative - "evolution is driven by relative fitnesses, not absolute fitnesses. Santayana's aphorism, ``It is not enough to succeed; others must fail.''
At any time, an organism's chances of surviving depend not on how fit it is, but on how fit it is relative to its competition."
http://www.swintons.net/deodands/archives/cat_neutron_teaspoon.html
Neutron stars do really exist. Long after the protons and electrons have long given up the struggle to maintain their identity against the force of gravity, all that is left is neutrons, pressed together into one big atomic nucleus a few kilometres across.
Stars are big balls of gases. Their size is determined by the balance between two opposing forces: gravity pulling the gas inwards, and pressure pushing it outwards. Just like the pressure of air in a balloon, pressure reflects the fact that it's hard to push things together. The pressure depends on how many things you're trying to push together (density), but it also depends on how hard they are to push together. At higher temperatures, the air molecules have more energy, so it takes more effort to keep them from bouncing off each other. There's a relation, then, between the amount of matter and the pressure it exerts in a given setting, which is called the equation of state. We have a fairly good idea of this relationship for the interior of stars like our own sun. Eventually, as our sun radiates energy away, the internal pressure will fall and the gravitational force will increase the density until the point at which electrons are forced together (or, more precisely into degenerate states) forming a white dwarf, and for these conditions we also have a fairly good idea of the equation of state. But for more massive stars, the collapse keeps going past this point and is only halted when the remaining neutrons are forced too 'close' together. And at this point we reach some uncertainty (at least according to 1980 era graduate texts) in what the equation of state is. So there is some real scientific uncertainty in the mass of the neutron teaspoon.
Tuesday, August 18, 2009
Icosa + Octa + Tet = ICTET
Novel structure incorporating 3 simplest structural polyhedral forms:
" the ARC in =4D= " the tail as a rotating/fused/swiveling structure
I found 6 correlations. [Update: a 7th found, the Proxigean extreme spring tide occurs every 31 years, see bottom of post.] The last one was hard, the ictet has 31 sides, but what was the 12? I knew there must be a twelve. Then I remembered Bucky's 12 radial spokes supporting a tensional wheel. Just as a rotating tail (but not a swiveling tail) such as a propeller or a clock must balance outwards to avoid offset erosion of the prop axle, the wheel must have 12 contacts in balance, as the sphere in a matrix must have 12 contact points. The result is extraordinary. (I did not originally see the link of 31 GC & vertebral nerve prs and 12 cranial nerves, Rybo at Synergeo group did, a copy of his graphic is at the bottom of the ARC blog. Ken at AAT group noted the 31 equal temperment of an octave.)
1 growth-31 vert neural pairs, 12 cranial nerve pairs, pentameric
2 form-31 great circles in icosa, 12 vertices, pentagonal
3 energy-31 equal temperment in octave, 12 tones, pentatonic
4 time-31~ day/night cycles in month, 12 month, heptapent
5 triax-31=sum of 1st 7 factors, of 12 factors of 60, hexapent
6 ictet-31 triangular sides, 12 deg. of freedom of tail pentabase
7 orbit-31 year cycle extreme proxigean spring tide, 12 pt ellipsis
Bio video of helical propelled bacteria: Rhodobacter sphaeroides
http://www.rowland. harvard.edu/ labs/bacteria/ showmovie. php?mov=rsphe_ f_swim_1
http://tinyurl. com/qzdb4r
Good graphical explanation of flagella, cilia, rod:
http://lecturer. ukdw.ac.id/ dhira/BacterialS tructure/ Flagella. html
Note: (Flower petals/leaves often split as 2, 3, 5, which are prime)
The number 60, a highly composite number, has twelve factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
1 + 2 + 3 + 4 + 5 + 6 + 10 = 31 (sum of 1st 7 factors)
In spherically arranged tight-fit ball packing layers:
12, 42, 92, 162, 252, 362 (shell layer balls in VE, Icosa)
10, 40, 90, 160, 250, 360 (subtract 2)
1, 4, 9, 16, 25, 36 (divide by 10)
f = 1, 2, 3, 4, 5, 6 (sq root)
form: 1 tet = 4 sides (tetrahedron)
form: 1 octa = 8 sides (octahedron)
form: 1 octet = 11 sides (2 merge into 1 double pane = tube)
form: 1 icosa = 20 sides (icosahedron)
form: 1 ictet = 31 sides (icosa w/ pin-hinged octet "tail")
Ictet = icosa + tail, polar moment, mono-axis
So now we have a composite structure of all 3 structural elements, the overall shape is an icosa-spheroid with an octet tail which can rotate in any direction (or if reversely docked, swing-hinge in an arc), answering the question, from whence did the flagella and sperm arise. Also explains the persistence of the tail in all motile organisms. Also explains why humans have 31 vertebral neural pairs, 12 cranial neural pairs and no tail. At least it would seem so.
AFAIK no one has noted the significance of the combined 'Ictet' structure as a universal jointed spheric mobile entity, and its numerical parallel of 31 sides with the 31 equal temperment of the octave, the 31 vertebral neural pairs in humans, the 31 lunar days and 31 great circles of the icosahedron, the 31 sum of 1st 7 factors of 60.
http://www.tabletoptelephone.com/~hopspage/Fuller.html
http://en.wikipedia.org/wiki/Icosahedron
http://www.buckminster.info/Pics/Tetrahedra/Tet-Quark-Mite.gif
At the single open vertex of the tetrahedron (the far left blue point) of the octet is the universal 'pin joint' which is attached to one of the 12 pentagonal sutures (pore/window) of the (truncated/regular) icosahedron or hexapent buckyball, the octet tail allowed to swivel radially or horizontally on a favorable plane.
(The picture includes the internal electrostatic bonding forces referred to as a mite or quark, whose form is an irregular tetrahedron.)
Note that the icosa meets the octet at a pentagon window, the tet meets the octa with each of the tet base corners having 5 vectors. So there is a continuum of pentagonal adhesion/cohesion, aka pentabase. Synergetic.
DDeden, August 18, 2009
(ictet not abbreviation for interpenetrated icosa-tet, rather an abbreviation for attached icosa-octa-tet, in the manner of R.B. Fuller term octet to name attached octa-tet form in patent.)
(More information on ICTET 31-12 available at AAT & Synergeo Yahoo groups.)
-
background addendum:
The term harmony derives from the Greek (harmonía), meaning "joint", re. "to fit
together, to join". The harmonious major triad is composed of three tones in a
simple whole number ratio of 6:5:4. The major triad chord in music theory
consists of a root, a major third, and a perfect fifth.
In structural theory, the simplest closed structures, the Platonic triad, are
the tetrahedron, the octahedron and the icosahedron. It would seem to me that
these 2 triads or chords are the same relationship expressed in different form,
(sound) energy and physical matter. [Compare to diving/backfloating partners
with infant]
The relevance to the 'ictet' above is that the chordal form triad is
preserved, the icosa, tet and oct are securely joined, yet the pin joint allows
vibrational energy propulsion via propeller rotation equivalent to a wheel of 12 spokes tensionally held or 12 degrees of freedom. A dual pin hinge would produce lateral swiveling.
An alternative form, not considered here but perhaps relevant to echinoforms or
spongiforms, is a central icosa with an octet flagella (or spine) docked at each
of the 12 surface pentagons, resembling a stellated icosahedron.
Tetrahedron: triangular corner (3 lines converge)
Octahedron: square corner (4 lines converge)
Icosahedron: pentagon corner (5 lines converge)
Potentially supporting information as to the antiquity of the ictet tail structure, this time as a fused external structure: fused structural segments produce 'primary cilia' (flagella, filament) different from motile cilia and found in animal skin and brain cells. Not impossibly this 'primary cilia' became the source of the notochord & tail in pre/vertebrates.
-
http://www.eurekalert.org/pub_releases/2009-08/uoc--ssc082109.php
"Unlike the more familiar motile cilia, primary cilia do not move, and only one pokes out of each cell. They have recently been discovered to play an essential role in assuring normal embryological development. May protect against skin cancer"
http://www.eurekalert.org/pub_releases/2009-08/uoc--sbt082109.php
"UCSF scientists have discovered that a tiny filament extending from cells, until recently regarded as a remnant of evolution, may play a role in the most common malignant brain tumor in children. "In the last few years, primary cilia have been shown to be essential for the cell-signaling that drives both human development, including the differentiation of stem cells into neurons, and some diseases, including polycystic kidney disease. The fact that the two UCSF studies implicate primary cilia in two totally different tissues suggests the finding is likely to be very general."
Note: A skew icosahedron is inscribed within an octahedron in a 4 frequency tetrahedron.
http://groups.yahoo.com/group/synergeo/message/54332
"In other words, you can't make a regular icosahedron out of regular tetrahedrons. In
http://groups.yahoo.com/group/synergeo/message/10326
I once said that, "The dihedral angle between the faces of a regular tetrahedron is 1.230959418 radians or 70.52877938 degrees. This is also the angle between alternating faces of a regular octahedron. Notice that it is not quite 72 degrees, so you can't put exactly five
tetrahedra around a common edge or five octahedra around a common vertex, as was attempted in the gapball or octaball Photos." AM
http://home.usit.net/~rybo6/rybo/id2.html
-
The number 31 pops up again, this time in regard to tidal cycles.
"During the last 400 years, there have been 39 instances or 'Extreme Proxigean Spring Tides' There were, in fact cases of extreme tidal flooding recorded during these particular spring tides which occur once every 31 years."
1800 yr ocean tidal cycle
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=18099
The gravitational force of the moon is one ten-millionth that of earth, but when you combine other forces such as the earth's centrifugal force created by its spin, you get tides.
When the moon is full or new, the gravitational pull of the moon and sun are combined. At these times, the high tides are very high and the low tides are very low. This is known as a spring tide. The net result of this is that the Earth gets deformed into a slightly squashed, ellipsoidal shape due to these tidal forces.
The tidal bulge of the Moon follows along the path on the earth's surface which intersects with the orbital plane of the Moon. This plane is tilted about 23 degrees with respect to the equatorial plane of the earth. The result is that near the equator, the difference between high tide and low tide is actually rather small, compared to other latitudes.
The Proxigean Spring Tide is a rare, unusually high tide. This very high tide occurs when the moon is both unusually close to the Earth (at its closest perigee, called the proxigee) and in the New Moon phase (when the Moon is between the Sun and the Earth). The proxigean spring tide occurs at most once every 1.5 years.
During the last 400 years, there have been 39 instances or 'Extreme Proxigean Spring Tides' where the tide-producing severity has been near the theoretical maximum. The last one of these was on March 7 1995 at 22:00 hours Greenwich Civil Time during a lunar Full Moon. There were, in fact cases of extreme tidal flooding recorded during these particular spring tides which occur once every 31 years."
If you see earths' orbit as a circle (slightly lopsided, ellipse) around the sun, imagine the sun as the center of a sunflower, and earth orbit as the edge of that center, then the moon could be seen as a set of 366 flower petals around it. In the last 400 years, the extreme proxigean spring tide occurred 39 times. Maybe at 366 it skipped the extreme tide.
Also note Rybo's picture at bottom of page showing the 31 spinal nerve pairs and 12 cranial nerve pairs.
" the ARC in =4D= " the tail as a rotating/fused/swiveling structure
I found 6 correlations. [Update: a 7th found, the Proxigean extreme spring tide occurs every 31 years, see bottom of post.] The last one was hard, the ictet has 31 sides, but what was the 12? I knew there must be a twelve. Then I remembered Bucky's 12 radial spokes supporting a tensional wheel. Just as a rotating tail (but not a swiveling tail) such as a propeller or a clock must balance outwards to avoid offset erosion of the prop axle, the wheel must have 12 contacts in balance, as the sphere in a matrix must have 12 contact points. The result is extraordinary. (I did not originally see the link of 31 GC & vertebral nerve prs and 12 cranial nerves, Rybo at Synergeo group did, a copy of his graphic is at the bottom of the ARC blog. Ken at AAT group noted the 31 equal temperment of an octave.)
1 growth-31 vert neural pairs, 12 cranial nerve pairs, pentameric
2 form-31 great circles in icosa, 12 vertices, pentagonal
3 energy-31 equal temperment in octave, 12 tones, pentatonic
4 time-31~ day/night cycles in month, 12 month, heptapent
5 triax-31=sum of 1st 7 factors, of 12 factors of 60, hexapent
6 ictet-31 triangular sides, 12 deg. of freedom of tail pentabase
7 orbit-31 year cycle extreme proxigean spring tide, 12 pt ellipsis
Bio video of helical propelled bacteria: Rhodobacter sphaeroides
http://www.rowland. harvard.edu/ labs/bacteria/ showmovie. php?mov=rsphe_ f_swim_1
http://tinyurl. com/qzdb4r
Good graphical explanation of flagella, cilia, rod:
http://lecturer. ukdw.ac.id/ dhira/BacterialS tructure/ Flagella. html
Note: (Flower petals/leaves often split as 2, 3, 5, which are prime)
The number 60, a highly composite number, has twelve factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
1 + 2 + 3 + 4 + 5 + 6 + 10 = 31 (sum of 1st 7 factors)
In spherically arranged tight-fit ball packing layers:
12, 42, 92, 162, 252, 362 (shell layer balls in VE, Icosa)
10, 40, 90, 160, 250, 360 (subtract 2)
1, 4, 9, 16, 25, 36 (divide by 10)
f = 1, 2, 3, 4, 5, 6 (sq root)
form: 1 tet = 4 sides (tetrahedron)
form: 1 octa = 8 sides (octahedron)
form: 1 octet = 11 sides (2 merge into 1 double pane = tube)
form: 1 icosa = 20 sides (icosahedron)
form: 1 ictet = 31 sides (icosa w/ pin-hinged octet "tail")
Ictet = icosa + tail, polar moment, mono-axis
So now we have a composite structure of all 3 structural elements, the overall shape is an icosa-spheroid with an octet tail which can rotate in any direction (or if reversely docked, swing-hinge in an arc), answering the question, from whence did the flagella and sperm arise. Also explains the persistence of the tail in all motile organisms. Also explains why humans have 31 vertebral neural pairs, 12 cranial neural pairs and no tail. At least it would seem so.
AFAIK no one has noted the significance of the combined 'Ictet' structure as a universal jointed spheric mobile entity, and its numerical parallel of 31 sides with the 31 equal temperment of the octave, the 31 vertebral neural pairs in humans, the 31 lunar days and 31 great circles of the icosahedron, the 31 sum of 1st 7 factors of 60.
http://www.tabletoptelephone.com/~hopspage/Fuller.html
http://en.wikipedia.org/wiki/Icosahedron
http://www.buckminster.info/Pics/Tetrahedra/Tet-Quark-Mite.gif
At the single open vertex of the tetrahedron (the far left blue point) of the octet is the universal 'pin joint' which is attached to one of the 12 pentagonal sutures (pore/window) of the (truncated/regular) icosahedron or hexapent buckyball, the octet tail allowed to swivel radially or horizontally on a favorable plane.
(The picture includes the internal electrostatic bonding forces referred to as a mite or quark, whose form is an irregular tetrahedron.)
Note that the icosa meets the octet at a pentagon window, the tet meets the octa with each of the tet base corners having 5 vectors. So there is a continuum of pentagonal adhesion/cohesion, aka pentabase. Synergetic.
DDeden, August 18, 2009
(ictet not abbreviation for interpenetrated icosa-tet, rather an abbreviation for attached icosa-octa-tet, in the manner of R.B. Fuller term octet to name attached octa-tet form in patent.)
(More information on ICTET 31-12 available at AAT & Synergeo Yahoo groups.)
-
background addendum:
The term harmony derives from the Greek (harmonía), meaning "joint", re. "to fit
together, to join". The harmonious major triad is composed of three tones in a
simple whole number ratio of 6:5:4. The major triad chord in music theory
consists of a root, a major third, and a perfect fifth.
In structural theory, the simplest closed structures, the Platonic triad, are
the tetrahedron, the octahedron and the icosahedron. It would seem to me that
these 2 triads or chords are the same relationship expressed in different form,
(sound) energy and physical matter. [Compare to diving/backfloating partners
with infant]
The relevance to the 'ictet' above is that the chordal form triad is
preserved, the icosa, tet and oct are securely joined, yet the pin joint allows
vibrational energy propulsion via propeller rotation equivalent to a wheel of 12 spokes tensionally held or 12 degrees of freedom. A dual pin hinge would produce lateral swiveling.
An alternative form, not considered here but perhaps relevant to echinoforms or
spongiforms, is a central icosa with an octet flagella (or spine) docked at each
of the 12 surface pentagons, resembling a stellated icosahedron.
Tetrahedron: triangular corner (3 lines converge)
Octahedron: square corner (4 lines converge)
Icosahedron: pentagon corner (5 lines converge)
Potentially supporting information as to the antiquity of the ictet tail structure, this time as a fused external structure: fused structural segments produce 'primary cilia' (flagella, filament) different from motile cilia and found in animal skin and brain cells. Not impossibly this 'primary cilia' became the source of the notochord & tail in pre/vertebrates.
-
http://www.eurekalert.org/pub_releases/2009-08/uoc--ssc082109.php
"Unlike the more familiar motile cilia, primary cilia do not move, and only one pokes out of each cell. They have recently been discovered to play an essential role in assuring normal embryological development. May protect against skin cancer"
http://www.eurekalert.org/pub_releases/2009-08/uoc--sbt082109.php
"UCSF scientists have discovered that a tiny filament extending from cells, until recently regarded as a remnant of evolution, may play a role in the most common malignant brain tumor in children. "In the last few years, primary cilia have been shown to be essential for the cell-signaling that drives both human development, including the differentiation of stem cells into neurons, and some diseases, including polycystic kidney disease. The fact that the two UCSF studies implicate primary cilia in two totally different tissues suggests the finding is likely to be very general."
Note: A skew icosahedron is inscribed within an octahedron in a 4 frequency tetrahedron.
http://groups.yahoo.com/group/synergeo/message/54332
"In other words, you can't make a regular icosahedron out of regular tetrahedrons. In
http://groups.yahoo.com/group/synergeo/message/10326
I once said that, "The dihedral angle between the faces of a regular tetrahedron is 1.230959418 radians or 70.52877938 degrees. This is also the angle between alternating faces of a regular octahedron. Notice that it is not quite 72 degrees, so you can't put exactly five
tetrahedra around a common edge or five octahedra around a common vertex, as was attempted in the gapball or octaball Photos." AM
http://home.usit.net/~rybo6/rybo/id2.html
-
The number 31 pops up again, this time in regard to tidal cycles.
"During the last 400 years, there have been 39 instances or 'Extreme Proxigean Spring Tides' There were, in fact cases of extreme tidal flooding recorded during these particular spring tides which occur once every 31 years."
1800 yr ocean tidal cycle
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=18099
The gravitational force of the moon is one ten-millionth that of earth, but when you combine other forces such as the earth's centrifugal force created by its spin, you get tides.
When the moon is full or new, the gravitational pull of the moon and sun are combined. At these times, the high tides are very high and the low tides are very low. This is known as a spring tide. The net result of this is that the Earth gets deformed into a slightly squashed, ellipsoidal shape due to these tidal forces.
The tidal bulge of the Moon follows along the path on the earth's surface which intersects with the orbital plane of the Moon. This plane is tilted about 23 degrees with respect to the equatorial plane of the earth. The result is that near the equator, the difference between high tide and low tide is actually rather small, compared to other latitudes.
The Proxigean Spring Tide is a rare, unusually high tide. This very high tide occurs when the moon is both unusually close to the Earth (at its closest perigee, called the proxigee) and in the New Moon phase (when the Moon is between the Sun and the Earth). The proxigean spring tide occurs at most once every 1.5 years.
During the last 400 years, there have been 39 instances or 'Extreme Proxigean Spring Tides' where the tide-producing severity has been near the theoretical maximum. The last one of these was on March 7 1995 at 22:00 hours Greenwich Civil Time during a lunar Full Moon. There were, in fact cases of extreme tidal flooding recorded during these particular spring tides which occur once every 31 years."
If you see earths' orbit as a circle (slightly lopsided, ellipse) around the sun, imagine the sun as the center of a sunflower, and earth orbit as the edge of that center, then the moon could be seen as a set of 366 flower petals around it. In the last 400 years, the extreme proxigean spring tide occurred 39 times. Maybe at 366 it skipped the extreme tide.
Also note Rybo's picture at bottom of page showing the 31 spinal nerve pairs and 12 cranial nerve pairs.
Saturday, April 4, 2009
Aquanautical microbiota: Green Algae
Spirogyra reproduction, reminds one of double helix DNA, chromosome replication
Dancing spheres: volvox rotates, oscillates
Volvox reproduction, note the triangulation of cytoplasm threads, geodesic structure
volvox A large sphere colony with daughter sphere colonies containing small granddaughter colonies. Both male and female colonies form inside the equator of the parent colony. Volvoxes are hollow spheres of independent cells that each have an eye spot, the colony develops a light-polarity, where half of the colony has larger eye spots, making a supercell eyeball of sorts. Click the link to find out more. volvox wikipedia
nuther volvox tale
Pediastrum algae, a flat disk star
These outstanding photos are from this site: The Micropolitan Museum
Hydrodictyon reticulatum, Hexa-penta Water net algae, from: Hydrodictyon, Wikipedia
Protists: dinoflagellate plant/animal (planimal?) in toxic red tide, endosymbiont coral bleaching, some photosynthesizers and some with eyes (retina), have minicircles of 12 genes.
http://madlabrat.blogspot.com/2009/10/protists-and-their-plastids.html
Marimo Moss balls (Chladophora)
from cell to super-cell organism to super-organism society: colonial ants
-
Nutrition: Seaweed gardens
Naturally growing seaweeds are an important source of food, especially in Asia. They provide many vitamins including: A, B1, B2, B6, niacin and C, and are rich in iodine, potassium, iron, magnesium and calcium.[50] In addition commercially cultivated microalgae, including both Algae and Cyanobacteria, are marketed as nutritional supplements, such as Spirulina,[51] Chlorella and the Vitamin-C supplement, Dunaliella, high in beta-carotene.
Algae are national foods of many nations: China consumes more than 70 species, including fat choy, a cyanobacterium considered a vegetable; Japan, over 20 species;[52] Ireland, dulse; Chile, cochayuyo.[53] Laver is used to make "laver bread" in Wales where it is known as bara lawr; in Korea, gim; in Japan, nori and aonori. It is also used along the west coast of North America from California to British Columbia, in Hawaii and by the Māori of New Zealand. Sea lettuce and badderlocks are a salad ingredient in Scotland, Ireland, Greenland and Iceland.
Dulse, a food.
The oils from some Algae have high levels of unsaturated fatty acids. For example, Parietochloris incisa is very high in arachidonic acid, where it reaches up to 47% of the triglyceride pool.[54] Some varieties of Algae favored by vegetarianism and veganism contain the long-chain, essential omega-3 fatty acids, Docosahexaenoic acid (DHA) and Eicosapentaenoic acid (EPA), in addition to vitamin B12. The vitamin B12 in algae is not biologically active. Fish oil contains the omega-3 fatty acids, but the original source is algae, which are eaten by marine life such as copepods and are passed up the food chain.[55] wikipedia: algae nutrition
Tuesday, October 7, 2008
Symmetry, Scale, Force, Structure, System
Finally, the basic fundamental forces in the universe appear to be related on a very deep level. They're really the same thing, but operating at different scales and different energy levels. At very high energy levels, electromagnetic forces, and the two atomic forces are all really the same thing. There's a deep symmetry between them. But as the energy level of the environment goes down, eventually they split, and become distinguishable. The symmetry breaks, and we get different forces.
Symmetry, forces, scale
Simplest 3D symmetrical planar prime structure systems in universe: Tetrahedron, then octahedron & icosahedron. tetrahedra
icosahedra
Simplest 2D symmetrical planar structure in universe: Triangle triangles
Simplest 3D symmetrical nonplanar structure in universe: Sphere
http://www.angelfire.com/mt/marksomers/125.html
Simplest 2D symmetrical nonplanar structure in universe: Circle
Simplest 3D nucleated vector equilibrium system: Cuboctahedron
VE
Simplest 3D grid octet truss space frame: Isotropic Vector Matrix
IVM
Freeze Frame: Tetrahedral simplest rigid structure.
Pea & toothpick tet
Fluid Frame: Spherical simplest structure.
waterball in space
duo-tet: doubled center ~ high gravity nucleus
Jitterbug transformation from VE thru Icosa to Octa:
Click here to see jitterbug transform
(Images from Synergeo and Synergetics on the web)
Symmetry, forces, scale
Simplest 3D symmetrical planar prime structure systems in universe: Tetrahedron, then octahedron & icosahedron. tetrahedra
icosahedra
Simplest 2D symmetrical planar structure in universe: Triangle triangles
Simplest 3D symmetrical nonplanar structure in universe: Sphere
http://www.angelfire.com/mt/marksomers/125.html
Simplest 2D symmetrical nonplanar structure in universe: Circle
Simplest 3D nucleated vector equilibrium system: Cuboctahedron
VE
Simplest 3D grid octet truss space frame: Isotropic Vector Matrix
IVM
Freeze Frame: Tetrahedral simplest rigid structure.
Pea & toothpick tet
Fluid Frame: Spherical simplest structure.
waterball in space
duo-tet: doubled center ~ high gravity nucleus
Jitterbug transformation from VE thru Icosa to Octa:
Click here to see jitterbug transform
(Images from Synergeo and Synergetics on the web)
Friday, September 26, 2008
the arc
Honorable Mention, Illustration: "Visualizing the Bible"
http://news.nationalgeographic.com/news/2008/09/photogalleries/2008-best-science-photos/photo6.html
Also see my other blog for nice pics of "the arc": http://dudescoffeeblender.blogspot.com/2008/09/arc-anciel-httpwww.html
And to cap off this post, a quote from Kelly's blog: "Okay, Patience: Across the arc of a life lived in faith, it allows the Almighty to be all-mighty." from "Flabbergasted" by Ray Blackston
[I have no idea of the context, but it's a cool quote! Cheers!]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Couple late links on Charles Darwin, Naturalist:
His tree of life: "I Think"
His faith & marriage: "I Do"
His r'evolutionary idea: "I Am"
Language and gesture: http://cas.bellarmine.edu/tietjen/Ec&Ev_Distance_learning/BehavLab/evolved_human_behaviors.htm
Subscribe to:
Posts (Atom)