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→Key and Explanations
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Euler's formula for Zeta-function: | Euler's formula for Zeta-function: | ||
: $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ | : $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ | ||
*I. Jones polynomial for right trefoil knot; Witten’s path-integral formulation for Jones polynomial using Chern-Simons action | |||
*II. Associativity equation in Quantum Field Theory | |||
*III. Yang-Baxter equation | |||
*IV. Lorenz Attractor: Lorenz equations with orbit | |||
*V. Diagram of a black hole with Schwarzschild radius | |||
*VI. The five regular polyhedra | |||
*VII. Equiangular spiral drawn in "golden" rectangle (side ratio = golden mean g), ratio of consecutive Fibonacci numbers approaches g, represented by is continued fraction expansion. | |||
*VIII.Babylonian computation of sqrt2 | |||
*IX. Visual proof of the Pythagorean Theorem | |||
*X. Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula. | |||
*XI. Archimedes: volume of Sphere. | |||
*XII. Aharanov-Bohm effect | |||
*XIII.Supergravity Langangian; root diagramm for Lie group E8 | |||
*XIV. Navier-Stokes equation with flow around cylinder. | |||
*1. Kepler's 2nd law. | |||
*2. Newton's force-acceleration equation. | |||
*3. Kepler's 3rd law | |||
*4 Newton's gravitational law | |||
*5 Einstein's General Relativity equation | |||
*6 Schrödinger's equation | |||
*7. Dirac equation | |||
*8. Atiyah-Singer Theorem. | |||
*9. Yang-Mills Equations | |||
*10. Defining relation of Supersymmetry | |||
*A. Einstein’s mass-energy equation | |||
*B. Maxwell's Equations | |||
*C. Stoke's Theorem | |||
*D. The boundary of a boundary is zero | |||
*E. Heisenberg's indeterminacy relation. | |||
*F. Euler's formula for Zeta-function. | |||
*G. Interaction between two string; Feynman diagram shows corresponding interaction of particles, here the Compton scattering of a photon off an electron. | |||