Latex-Beamer: Create Rooty Helix

rooty-helix.tex

% Rooty helix
% Author: Felix Lindemann
\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\pagestyle{empty}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\xdefinecolor{darkgreen}{RGB}{175, 193, 36}
\newcounter{cntShader}
\newcounter{cntRoot}
\setcounter{cntShader}{20}
\def\couleur{darkgreen}

\begin{tikzpicture}
    \foreach \y in {86,38,15}{
        \setcounter{cntShader}{1}
        \coordinate (a) at (0,0);
        \coordinate (b) at (0:1);
        \foreach \x in {1,...,\y}{%
            \coordinate (c) at ($ (b)!1cm!270:(a) $);
            \begin{pgfonlayer}{background}
                \draw[fill=\couleur!\thecntShader] (a)--(b)--(c)--cycle;
            \end{pgfonlayer}
            \setcounter{cntRoot}{\x}
            \addtocounter{cntRoot}{1}
            \node[fill=white,draw,circle,inner sep=1pt] at (c)
                {$\sqrt{\thecntRoot}$};
            \coordinate (b) at (c);
            \pgfmathsetcounter{cntShader}{\thecntShader+4}
            \setcounter{cntShader}{\thecntShader}
       }
    }
    \node[fill=white,draw,circle,inner sep=1pt] at (0:1) {$\sqrt{1}$};
\end{tikzpicture}

\end{document} 

Thanks for the cool script. Can you please explain how you selected the numbers 86, 38 and 15?

Thanks for the cool script. Can you please explain how you selected the numbers 86, 38 and 15?

Hi, thank you for your reply... after both 15 and 38 full circles were drawn and I had to draw these afterwards on top because as far as I know layers are not supported. the 86 was the age of my grandfather whom I gave this as a birthday present.