Consider a rectangular piece of paper ABCD with AB ≠ AD

Show how you can fold this piece of paper into five pieces of equal area.

*** Using any given instrument like straightedge, compass, protractor, ruler etc. is NOT permissible.

I was trying to draw my previous solution and I came across an idea that renders moot what Steve and I were discussing.

All you need is 5 equal spaces on part of one side and a diagonal line through them.

Fold B and C less than a fifth of the way to A and D (creates a narrow rectangle.)  
Repeat 4 more times and unfold.
Call the point where the last of these creases meet edge CD by I
Make crease IB.
This new crease crosses 4 of the 5 creases that are parallel to BC.  They do so at points 1/5, 2/5, 3/5 and 4/5 of the way from edge AB to CD.
So we are basically done.
Just fold C and D towards B and A such that the crease passes through each of these 4 points and you have 5 equal rectangles.

(This solution works for any aspect ratio rectangle.)

Posted by Jer on 2014-04-27 01:21:40