Given a partition of a square into n triangles of equal area, prove that n is even.

(In reply to re(2): Equal area, congruent triangles. by Richard)

"It is not possible to dissect a square into an odd number of equal area triangles.  If we can dissect a unit square into an odd number, n, of rectangles, then each rectangle has area 1/n, and since n is an odd integer, |1/ n|₂ <= 1.  We will show that we must have |1/n|₂> 1, so this will prove the result."

Here's a link to the rest of the proof by Paul Monsky:

http://www.math.lsu.edu/~verrill/teaching/math7280/triangles.pdf

Edited to replace "¡Ü" with "<=". Apparently, the greater than or equal to symbol from the format tool above the comment area does not always display properly.

Edited on February 5, 2006, 12:52 pm

Posted by Mindrod on 2006-02-05 02:07:14