# Example: Pascal triangle

Published 2016-12-30 | Author: M.H. Ahmadi

A calculated Pascal triangle built with hexagons.

Download as: [PDF] [TEX]  •  [Open in Overleaf]

Do you have a question regarding this example, TikZ or LaTeX in general? Just ask in the LaTeX Forum.
Oder frag auf Deutsch auf TeXwelt.de. En français: TeXnique.fr.

% Pascal triangle
% Author: M.H. Ahmadi
\documentclass[border=10pt]{standalone}%
\usepackage[dvipsnames]{xcolor}
\usepackage{tikz}
\usepackage{ifthen}
\makeatletter
\newcommand\binomialCoefficient[2]{%
% Store values
\c@pgf@counta=#1% n
\c@pgf@countb=#2% k
%
% Take advantage of symmetry if k > n - k
\c@pgf@countc=\c@pgf@counta%
\advance\c@pgf@countc by-\c@pgf@countb%
\ifnum\c@pgf@countb>\c@pgf@countc%
\c@pgf@countb=\c@pgf@countc%
\fi%
%
% Recursively compute the coefficients
\c@pgf@countc=1% will hold the result
\c@pgf@countd=0% counter
\pgfmathloop% c -> c*(n-i)/(i+1) for i=0,...,k-1
\ifnum\c@pgf@countd<\c@pgf@countb%
\multiply\c@pgf@countc by\c@pgf@counta%
\advance\c@pgf@counta by-1%
\advance\c@pgf@countd by1%
\divide\c@pgf@countc by\c@pgf@countd%
\repeatpgfmathloop%
\the\c@pgf@countc%
}
\makeatother
\begin{document}
\newdimen\R
\R=.4cm
\newcommand\mycolor{gray}
\begin{tikzpicture}[line width=.8pt]
\foreach \k in {0,...,12}{
\begin{scope}[shift={(-60:{sqrt(3)*\R*\k})}]
\pgfmathtruncatemacro\ystart{12-\k}
\foreach \n in {0,...,\ystart}{
\pgfmathtruncatemacro\newn{\n+\k}
\ifthenelse{\k=0}{\def\mycolor{pink}}{}
\ifthenelse{\k=1}{\def\mycolor{yellow}}{}
\ifthenelse{\k=2}{\def\mycolor{blue}}{}
\ifthenelse{\k=3}{\def\mycolor{green}}{}
\ifthenelse{\k=8 \AND \n < 4}{\def\mycolor{purple}}{}
\ifthenelse{\k=9 \AND \n = 3}{\def\mycolor{purple}}{}
\begin{scope}[shift={(-120:{sqrt(3)*\R*\n})}]
\draw[top color=\mycolor!20,bottom color=\mycolor!60]
(30:\R) \foreach \x in {90,150,...,330} {
-- (\x:\R)}
-- cycle (90:0)
node {\tiny $\mathbf{\binomialCoefficient{\newn}{\k}}$};
\end{scope}
}
\end{scope}
}
\end{tikzpicture}
\end{document}


## Comments

Adding comments is currently not enabled.