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