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Phil's Polygonal Diameter Theorem
Given a 2n-gon...
You are to draw n diagonals so that they don't share end points, and there are an odd number of polygon sides between the end-points.
( - ) n ( + ) ( - ) Variants ( + ) In how many ways can you do this?
For n = 3 and 4, there is only one way.
For n = 5, there are 4 ways.
For n = 6, there are 9 ways.
For n = 7, there appear to be 43 ways
For n = 8, there appear to be 198 ways, and
For n = 9, there appear to be 1435 ways!
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©2023 Compass Learning Technologies ← Saltire Software → Phil's Polygonal Diameter Theorem