Dreaming In Latex

Coding The Scores Of The Tune Of Mathematics

There are many beautiful equations we can compose from the scribbly and seemingly obscure scripts of Latex.

\begin{align*}
    \text{Gou-Gu theorem, 勾股定理 (Pythagorean Theorem):} 
       \quad & a^2 + b^2 = c^2 \\
\text{Pythagorean, 570 BC} \\
\\
    \text{Logarithms:} 
       \quad & \log_b(xy) = \log_b(x) + \log_b(y) \\
       \quad & \log(xy) = \log(x) + \log(y) \\
\text{ John Napier, 1610} \\
\\
    \text{Calculus: Derivative:} 
     \quad & \frac{d}{dx}(f(x)) \lim_{x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x}\\

    \text{Integral:} 
     \quad & \int_{a}^{b} f(x) \,dx \\
\text{ Isaac Newton, 1668} \\
\\

    \text{Law of Gravity:} 
     \quad & F = G \frac{m_1 m_2}{r^2} \\
\text{ Isaac Newton, 1667} \\
\\
    \text{The square root of -1 (Imaginary Unit):} 
     \quad & i = \sqrt{-1} \\
\text{ Euler, 1750} \\
\\
    \text{Euler's Polyhedra Formula:} 
     \quad & V - E + F = 2 \\
\text{ Euler, 1751} \\
\\
    \text{Normal Distribution:} 
     \quad & f(x|\mu,\sigma^2) = \frac{1}{\sigma \sqrt{2\pi}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} } \\
\text{ C.F. Guass, 1810} \\
\\
    \text{Wave Equation:} 
     \quad & \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2} \\
\text{ J. d'Almbert, 1746} \\
\\
    \text{Fourier Transform:} 
     \quad & \hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)…