torus_expolain_formula.md

In this formula, ( R ) represents the radius from the center of the torus tube to the center of the torus, ( r ) is the radius of the tube, and ( u, v ) are the parameters that vary along the angles of the torus. If you need any further explanation or help with LaTeX, I’m at your disposal.

$$\begin{align*} x(\theta, \phi) &= (R + r \cos \theta) \cos \phi \\ y(\theta, \phi) &= (R + r \cos \theta) \sin \phi \\ z(\theta, \phi) &= r \sin \theta \end{align*}$$

begin{align*} x(\theta, \phi) &= (R + r \cos \theta) \cos \phi \ y(\theta, \phi) &= (R + r \cos \theta) \sin \phi \ z(\theta, \phi) &= r \sin \theta \end{align*}

$$\documentclass{article} \usepackage{xcolor} % Package for colors

\definecolor{githubblue}{HTML}{0366d6} % Defining the GitHub blue color

\begin{document}

[ \color{githubblue} \begin{align*} x(u, v) &= (R + r \cos v) \cos u \ y(u, v) &= (R + r \cos v) \sin u \ z(u, v) &= r \sin v \end{align*} ]

\end{document}$$