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Square of Triangles (Posted on 2006-02-04) Difficulty: 4 of 5
Given a partition of a square into n triangles of equal area, prove that n is even.

No Solution Yet Submitted by Josh70679    
Rating: 2.0000 (2 votes)

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re(4): Odd | Comment 19 of 21 |
(In reply to re(3): Odd by brianjn)

Not quite.  Rather than trying to partition the square.  I am suggesting starting with the triangles and showing that it is impossible for them (them being of odd number and equal in area of course) to be fitted together into a square with no holes because of the right angle count.

Edit: right angles are of course just a shorthand I am using for the interior angles of the triangles and my usage not imply that the triangles need  be either right angled or conguent.

Edited on February 5, 2006, 6:35 pm
  Posted by goFish on 2006-02-05 18:28:12

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