I. Jones Polynomial; Witten’s Path-integral Formulation

V_{K}(t) = (t + t^{3} − t^{4})(t^{\frac{1}{2}} + t^{− \frac{1}{2}} )

V_{K}(e^{\frac{2πi}{k+2}} ) = −\frac{1}{Z} ∫_{A} Tr (P exp ∮_{K} A) e^{\frac{ik}{4π} CS(A)} DA

II. Commutation relation

C_{ijk}η^{kl}C_{lmn} = C_{mjk}η^{kl}C_{lin}

III. Braid Relation

R_{12}R_{23}R_{12} = R_{23}R_{12}R_{23}

IV. Equations for Lorenz attractor:

\frac{dx}{dt} = σ(y − x)

\frac{dy}{dt} = x(ρ − z) − y

\frac{dz}{dt} = xy − βz

V. Black hole radius

r_{S} = 2Gm/c^{2}

VI. Platonic Solids VII. Golden mean = partial fraction expansion:

lim_{n→∞} \frac{F_{n+1}}{F_{n}} = 1 + \frac{1}{1 + …}

VIII. Babylonian calculation of \sqrt{2}

1; 24; 51; 10 = 1.414213 IX. Pythagorean Theorem

c^{2} = a^{2} + b^{2}

X. Archimedes’ calculation of volume, area of sphere

v = \frac{2}{3}V

a = \frac{2}{3}A

XI. Euler characteristic, Gauss-Bonnet Theorem

2πχ = ∫_{M} K dA

XII. Aharonov-Bohm Effect

∫_{C_{1}} A · dℓ − ∫_{C_{2}} A · dℓ = Φ

XIII. Supergravity potential

L = R − ψ̄_{μ}γ^{μρσ}D_{ρ}ψ_{σ}

XIV. Navier-Stokes Equation for Fluid Flow

ρ(∂_{t}v_{i} + v_{j}∂_{j}v_{i})

= −∂_{i}p + μ∂_{j}∂_{j}v_{i}