Re: Dissecting a square into triangles of equal area

On Sep 17, 4:05 pm, Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article <0d0te3l2c6c37koogjg6bemnv3g3skt...@xxxxxxx>, Angus Rodgers <twir...@xxxxxxxxxxx> wrote:

The following problem seems to be going the rounds (this
is the exact wording as it was presented to me):

Take a square. Draw any number of line segments in the
square to split in into n triangles, each with the same
area, with no area left over. Prove that n is even.

I'm told that a solution has been posted on the Web, at:
<http://www.math.lsu.edu/~verrill/teaching/math7280/triangles.pdf>
but I haven't looked at it, because I'm still struggling
with the problem (although after spending about an hour
on it a day for the last five days, my struggles may be
weakening).

I haven't looked at the site you cite. The result is generally
attributed to Monsky:

P. Monsky, On dividing a square into triangles, Amer. Math. Monthly 77
(1970) 161--164. MR0252233 (40 #5454)

That's what's in the PDF file: that paper. (Yes I peeked ... I am so
ashamed of myself; I should have thought of it myself. 8-( )

--- Christopher Heckman

.

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