Re: United Airlines magazine has surprisingly hard geometry problem

From: David Bernier (david250_at_videotron.ca)
Date: 07/29/04 

Date: Thu, 29 Jul 2004 15:22:16 -0400

Bart Goddard wrote:

>
>>Embedding the picture into a regular polygon? That's interesting. One
>>friend I showed it to immediately thought of treating the triangle as
>>one "wedge" of a regular 18-gon, and I think that he concluded that if
>>lines CD and AE were extended, they would be diagonals of the 18-gon.
>>But he didn't see what to do after that. Can this approach be pushed
>>through?
>
>
> Along the same lines, I was thinking of drawing out the Morley
> picture (the extended one, like the second graphic at
> http://mathworld.wolfram.com/MorleysTheorem.html) and chasing
> down all the angles. I'm wondering if the central large equilateral
> triangle doesn't have a side which contains EF, or is parallel to it.

In a Math Arxiv preprint, math.MG/9508209 by Bjorn Poonen and Michael
Rubinstein entitled:
``The Number of Intersection Points Made by the Diagonals of a Regular
   Polygon",

the authors write on page 4 in paragraph 2:
" The classification of three-diagonal intersections also solves
   Colin Tripp's problem [15] of enumerating adventitious quadrilaterals,
   those convex quadrilaterals for which the angles formed by
   sides and diagonals are all rational multiples of Pi."

David Bernier

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