# Star of David in Pascal's Triangle

Yesterday, I learnt drawing simple TikZ diagrams.

In my opinion, defining nodes while connecting them will not look good.

\path[draw] (0, 0) node {A} -- (1,0) -- (1,1) node {B};


I define the nodes before connecting them, and the result is what I desire.

I overlooked the meaning of clipping in Meik Hellmund’s short TikZ tutorial.1 I constructed the diagram using the edge command.

Realising that $\displaystyle {n \choose k} = \frac{n!}{r! (n - r)!}$, one can easily see that

$\binom{n - 1}{k - 1} \binom{n}{k + 1} \binom{n + 1}{k} = \binom{n - 1}{k} \binom{n}{k - 1} \binom{n + 1}{k + 1}.$

1. See p.12 of the tutorial.

“It is often better to define named nodes first and connect them later, since then the paths are clipped around the notes…”