New blog post: Counting paths in convex polygons, 11011110.github.io/blog/2022/0

A simple coloring-based explanation for why there are exactly $$n2^{n-3}$$ non-crossing paths through all points of an $$n$$-gon, and exactly $$\tfrac{n}{4}(3^{n-1}+3)$$ through some of the points (counting a single point as a path).

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@11011110
Nice!

In the first diagram, should the top-right blue point be red (or the last two path steps changed)?

@bmreiniger Oops, you're right. Fortunately easy to fix.

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