Helicoid

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage{ifthen}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% File name: helicoid.tex
% Description: 
% A geometric representation of an helicoid is shown.
% 
% Date of creation: May, 28th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 223 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\tdplotsetmaincoords{60}{120}
%
\begin{tikzpicture}[tdplot_main_coords,scale=3]
    % Parametric equations of the surface
    \tikzmath{function equis(\u,\v) {return \u*cos(\v r);};}
    \tikzmath{function ye(\u,\v) {return \u*sin(\v r);};}
    \tikzmath{function zeta(\u,\v) {return \c*\v;};}
    % Parameter for the function
    \pgfmathsetmacro{\c}{1.0/(2.0*pi)}
    % Domain for the graph
    \pgfmathsetmacro{\uunoi}{-0.75}
    \pgfmathsetmacro{\uunof}{0.75}
    \pgfmathsetmacro{\vi}{-2.0*pi}
 
 
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