Helicoid

Edit and compile if you like:

\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}
	\pgfmathsetmacro{\vf}{2.0*pi}
	\pgfmathsetmacro{\step}{\uunoi+\vf/500}
	\pgfmathsetmacro{\stepn}{\vi+\vf/500}
	% The graph of the function
	\foreach \u in {\uunoi,\step,...,\uunof}{
		\draw[cyan,thick,opacity=0.25] plot[domain=\vi:\vf,smooth,variable=\v] ({equis(\u,\v)},{ye(\u,\v)},{zeta(\u,\v)});
	}
	\foreach \v in {\vi,\stepn,...,\vf}{
		\draw[cyan,thick,opacity=0.25] plot[domain=\uunoi:\uunof,smooth,variable=\u] ({equis(\u,\v)},{ye(\u,\v)},{zeta(\u,\v)});
	}
\end{tikzpicture}
%
\end{document}