Labeled Polygon Triangulations

sides

4

index

1

Two interpretations of the Catalan numbers are the number of ways to parenthesize an ordered sequence of numbers to be multiplied, two at a time, and the number of ways a polygon with

n+2

sides can be cut into

n

triangles. This Demonstration shows the equivalence of the two interpretations by labeling each polygon triangulation with the corresponding parenthesized expression.