Pascal's triangle in LaTeX, with pointing arrows

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Pascal's triangle in tikz

I tried making this in a tabular, and it sort of worked. But I was not able to insert any arrows. Is there any simple way to make the image below in LaTeX?

I.e., to make a version of Pascal's triangle in LaTeX, with arrows showing how the next row is made

Example of Pascal's triangle, desired output

If you make the triangle in TikZ, then you can use TikZ syntax to make the arrows. For the basic triangle, take a look at http://tex.stackexchange.com/q/17522/86 — Andrew Stacey, Oct 25 '11 at 12:47

score 13 · Accepted Answer · answered Oct 25 '11 at 14:59

You can have Tikz determine the numbers and draw the pascal triangle (given a depth) as follows:

\documentclass{article}
\usepackage{tikz}
\def\mkPascal#1{
  \begin{tikzpicture}
    \def\dx{20pt}
    \def\dy{30pt}
    \newcounter{i}
    \stepcounter{i}
    \node (\arabic{i}) at (0,0) {1};
    \foreach [count=\i] \x in {2,...,#1}{
      \pgfmathsetmacro{\lox}{\x-1}%
      \pgfmathsetmacro{\loxt}{\x-3}%
      \foreach [count=\j] \xx in {-\lox,-\loxt,...,\lox}{
        \pgfmathsetmacro{\jj}{\j-1}%
        \stepcounter{i}
        \pgfmathsetmacro{\lbl}{\lox!/(\jj!*(\lox-\jj)!)}
        \node  (\arabic{i}) at (\xx*\dx, -\lox*\dy) {\pgfmathint{\lbl}\pgfmathresult};
      }
    }
    \newcounter{z}
    \newcounter{xn}
    \newcounter{xnn}
    \pgfmathsetmacro{\maxx}{#1 - 1}
    \foreach \x in {1,...,\maxx}{
      \foreach \xx in {1,...,\x}{
        \stepcounter{z}
        \setcounter{xn}{\arabic{z}}
        \addtocounter{xn}{\x}
        \setcounter{xnn}{\arabic{xn}}
        \stepcounter{xnn}
          \draw [->] (\arabic{z}) -- (\arabic{xn});
          \draw [->] (\arabic{z}) -- (\arabic{xnn});
      }
    }
  \end{tikzpicture}
}
\begin{document}
  \mkPascal{8}
\end{document}

First the nodes are drawn in the triangle configuration and their labels are determined. Second, we loop over the nodes again to draw the arrows, one to each child. The final result is as follows:

Pascal Triangle of depth 8

Unforunately, due to the use of faculties to calculate the node labels, you can't draw Pascal triangles of more than 8 levels. This could probably be increased by using the recursive definition for n choose k instead of this one.

score 6 · Answer 2 · answered Oct 25 '11 at 15:44

6

You have a nice Pascal's triangle and Sierpinski triangle in TeXample.net

answered Oct 25 '11 at 15:44

Ignasi

136,588

score 5 · Answer 3 · edited Jul 18 '17 at 07:50

As @Andrew says, the best method would be to use tikz. A crude alternative is to put the arrows and numbers in alternating rows in a tabular environment.

\documentclass{article}
\begin{document}
\newcommand{\ap}{\ensuremath{\swarrow\,\searrow}}
\setlength{\tabcolsep}{0pt}
\begin{tabular}{ccccccccc}
  &     &     &      & 1   &      &      &     & \\
  &     &     &      & \ap &      &      &     & \\
  &     &     & 1    &     &  1   &      &     & \\
  &     &     & \ap  &     &  \ap &      &     & \\
  &     & 1   &      & 2   &      & 1    &     & \\
  &     & \ap &      & \ap &      & \ap  &     & \\
  & 1   &     & 3    &     &  3   &      & 1   & \\
  &\ap  &     & \ap  &     &  \ap &      & \ap & \\
1 &     & 4   &      & 6   &      & 4    &     & 1
\end{tabular}
\end{document}

Pascal's triangle in LaTeX, with pointing arrows

3 Answers3