tetrahedron Posted November 26, 2013 Report Posted November 26, 2013 Hi folks. Been away for a while doing (gasp) linguistics (don't tell mom!). My most recent news: it looks like the Leibniz Harmonic Triangle is responsible in equal measure for the mathematical motivation behind real structures of atoms defined by their Hamiltonians (as opposed to simple harmonic oscillator models which fail to capture at least half of what is going on). The Leibniz Triangle uses fractions instead of integers, and they sum upwards rather than downwards. Actually the Leibniz diagonals are easy to build up by simple rule- you chop off the 1's outer jacket from Pascal, you take 1/(1xnaturals), 1/(2xtriangulars), 1/(3xtetrahedrals), 1/(4xpentatopes) and so on. Not only this, but the Pascal and Leibniz numbers apply ORTHOGONALLY to each other. Pascal primarily maps to energy level, with combinatoric variations falling against deformations from a sphere. I already know that the primary mapping for Leibniz numbers falls upon deformation (as oscillator ratios)- but because their distribution is inverted relative to the default ellipsoid (sphere), I'm postulating that numerically we have to define a default hyperboloid. More speculatively that that, that the fuller model requires a tetrahedron, the center of which will have paraboloidal motivation. I'm not sure yet how to pattern the Leibniz and Pascal numbers here but they won't be in the center, and will be orthogonally disposed somewhere on vertices, edges, faces. Anyway, that's about it unless you want to hear about Zulu! Jess Tauber[email protected] Quote
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