©2023 Compass Learning TechnologiesSaltire Software → Phil's Polygonal Diameter Theorem

 

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.

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( - ) n ( + )
( - ) Variants ( + )

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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 TechnologiesSaltire Software → Phil's Polygonal Diameter Theorem