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

video short of film
h/t Kirby U @ synergeo

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.

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