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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(2): Odd | Comment 17 of 21 |
(In reply to re: Even by Richard)

My original idea was to start with n triangles, i.e. 2n right angles.

We need 4 for the corners and 4 for each interior point. 

However we can also add 2 RA by combining a one of the edges of a triangle with a point, so that for n=3, the "extra" point lies on an edge of one of the triangles but now we cannot achieve equal areas.

However I have not figured out how or if this can be generalised.

I suspect that for odd n with equal areas, because the number of right angles is not divisible by 4, they cannot be fitted into a square.


  Posted by goFish on 2006-02-05 17:09:44
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