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A Nameless Number

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Author:Len Smiley
Description: Triangle-free polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)-gon with n+2 labeled nodes, what is a(n), the number of ways of drawing non-intersecting diagonals so that no triangles are formed? This question resonates somewhat with the parallel universe of "triangle-free graphs." With a formulation using geometric recurrences, and Mathematica code for the sequence of the number of (non-crossing) diagonal placements in the (n+3)-gon with vertices 1, 2, ..., n+3 such that no triangles appear.

Levels: High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles
Math Topics: Constructions, Triangles and Other Polygons, Sequences and Sets

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