\documentclass[12pt]{article}
\newcommand{\vs}{\vspace{.1in}}
\newcommand{\ds}{\displaystyle}
\newcommand{\p}{\partial}
\newcommand{\Tr}{\rm Tr}
\usepackage[T1]{fontenc}
\usepackage{yfonts}
\usepackage{graphicx}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{amssymb}
\def\Dirac{\not\hspace{-1.25mm}\partial}
\def\DDirac{\not\hspace{-1.25mm}D}

\usepackage{amsfonts}
\usepackage{rawfonts}
\usepackage{amsxtra}
\usepackage{amscd}
\usepackage{amsthm}
\usepackage{eucal}

%\usepackage{tikz}
%\usetikzlibrary{arrows,decorations.pathmorphing,decorations.markings,trees,backgrounds,fit,calc,through}
\usepackage{slashed}
\input{prepictex}
\input{pictex}
\input{postpictex}
\begin{document}

{\bf I. LARGE FORMULAS}

\noindent{1. \it Primes and the zeta function:} 
$$ \prod_p \frac{1}{1-\frac{1}{p^s}} = 
\sum_{n=1}^{\infty}\frac{1}{n^s}$$


\vs

\noindent{7. \it Newton's Law of Gravitation:}
$$ F = \frac{\ds G m_1m_2}{\ds r^2}$$


\vs


\noindent{12. \it Maxwell's Equations in Vacuum:}


$$\begin{array}{l}
\nabla \cdot {\bf B}  = 0 \\
\nabla \times {\bf B}  = \frac{\ds 1}{\ds c}\frac {\ds \partial {\bf E}}
{\ds \partial t}\\
\end{array}~~~~~
\begin{array}{l}
\nabla \cdot {\bf E}  = 0 \\
\nabla \times {\bf E}  = -\frac{\ds 1}{\ds c}\frac{\ds \partial {\bf B}}
{\ds \partial t}\\
\end{array}~~~~~
\begin{array}{r}
\nabla \times {\bf E}  = -\frac{\ds 1}{\ds c}\frac{\ds \partial {\bf B}}
{\ds \partial t}\\
\nabla \cdot {\bf E}  = 0 \\


\end{array}$$

\vs 



\noindent{14. \it Einstein's General Relativity Equation: }
$$R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}  = 8 \pi T_{\mu\nu}$$

\vs

\noindent{16. \it Heisenberg Uncertainty Principle:}
$$\Delta x \Delta p \geq  \hbar/2$$

\vs

\noindent{22. \it Stokes' Theorem}
$$\int_{M}d\omega=\int_{\partial M}\omega$$

$$\int_{M}d\omega$$

$$=\int_{\partial M}\omega$$

\vs
\noindent{26. \it Classical Gauss-Bonnet Theorem:} 



$$
\chi (M^{2})= \frac{1}{2\pi}
\int_{M}K 
~dA 
$$







\vs
\noindent{xy. \it Kepler's Laws:} 

$$r\frac{d\theta}{dt} = \mbox{C}$$

$$ \oint dt~ \propto ~ (\mbox{r}_{\mbox{min}} + \mbox{r}_{\mbox{max}})^{\frac{3}{2}}$$

$$ \oint dt \propto  (\overline{r} + \underline{r})^{\frac{3}{2}}$$

$$ \oint dt \propto  (\overline{r} + \underline{r})^{3/2}$$

$$ T = ka^{\frac{2}{3}}$$

$$ T = ka^{2/3}$$
\vs


\noindent{xz. \it Hamilton's quaternion eq.:}

$$i^2 = j^2 = k^2 = ijk = -1$$
\vs

\noindent{xw. \it Conservation of energy-momentum:}

$$T^{\mu \nu}_{,~\nu} = 0 $$
\vs

\noindent{35. \it Yang-Mills equation}
$$F = dA + A \wedge A$$
\vs



\noindent{xu. \it Self-dual}
$$ \ast F = F$$
\vs

{\bf II SMALL FORMULAS IN IMAGE CAPTIONS}

\noindent{8. \it Pythagoras' Theorem with no-word proof:} 

$$c^2 = a^2 + b^2 $$



\vs

\noindent{xt. \it knot polynomial}
$$q + q^3 - q^4 $$

$$V_K(q) = q + q^3 - q^4 $$ 
\vs

\noindent{xs. \it Babylonian tablet}
$$1;24;51;10 = 1.414213\dots$$
\vs

\noindent{xr. \it Schwartzschild radius}
$$r_S = 2Gm/c^2$$ 

\vs


\noindent{xx. \it Equation for Lorenz attractor:} 

$$\frac{\ds dx}{\ds dt} = \sigma(y-x)$$
$$\frac{\ds dy}{\ds dt} = x(\rho-z) -y$$
$$\frac{\ds dz}{\ds dt} = xy - \beta z$$
\vs

\noindent{58. \it Platonic solids, Euler characteristic:}
$$ V - E + F = 2$$
\vs

\noindent{42. \it Navier-Stokes equation:}
$$  \p_t v_i + v_j \p_j v_i = -\p_i p + \nu \p_j \p_j v_i  $$
\vs

\noindent{2. \it Archimedes. Volume of Sphere:}

$$ v = \frac{2}{3}V$$
\vs

\noindent{19. \it Limiting ratio of Fibonacci numbers = golden mean
= partial fraction expansion:}
$$ \lim_{n\rightarrow\infty}\frac{\ds F_{n+1}}{\ds F_n}                         
= \frac{\ds 1 + \sqrt{5}}{\ds 2} = {1}+ \frac{\ds 1}{1+\frac{1}{1+              
\frac{1}{1+ \dots } }    }$$


$$  \frac{\ds 1 + \sqrt{5}}{\ds 2} = {1}+ \frac{\ds 1}{1+\frac{1}{1+              
\frac{1}{1+ \dots } }    }$$
\vs

\noindent{55. \it Aharonov-Bohm Effect:}

$$\int_{C_2} {\vec A}\cdot d{\vec\ell} - \int_{C_1} {\vec A}\cdot d{\vec\ell}  
= \frac{1}{2\pi}\Phi$$
\vs

\noindent{20. \it Wilson loop average w.r.t Chern-Simons action
gives knot invariant:}

$${1\over Z}   \int_{\mathcal A} \Tr_{\bf 2} P\exp{\!\left(-\oint_K A \right)}
\,  e^{\!{{i k}\over{4 \pi}} \, {\rm CS}(A)} {\mathcal D} A$$

$${1\over Z} \int_{\mathcal A} (\Tr_{\bf 2} P\oint_K A)\,
e^{\!{{i k}\over{4 \pi}} \, {\rm CS}(A)} {\mathcal D} A$$

$${1\over Z} \int_{\mathcal A} (\Tr_{\bf 2} P\oint_K A)\,
e^{\!{{i k}\over{4 \pi}} \, \int_M {\rm Tr}(A\wedge d A+    
\frac{2}{3}A\wedge A\wedge A)} {\mathcal D} A$$
\vs

\noindent{xq. \it Volume of frustum of pyramid (from Moscow Papyrus:)}

$$V = \frac{1}{3}\cdot 6(2^2 + 4^2 + 2\cdot 4) = 56$$
\vs

\noindent{3. \it Yang-Baxter Equation}
$$R_{12}R_{23}R_{12} = R_{23}R_{12}R_{23}$$


\end{document}

