Dividing a Square Cake into Five Equal Pieces
Date: 07/28/2001 at 10:48:48 From: Pam English Subject: Dividing regions of a square How can you divide a square-topped cake that is a rectangular solid and is frosted on all faces into five pieces so that everyone receives the same amount of cake and icing? All cuts must be perpendicular to the surface. I can not figure this out. All I can do is divide the cake four ways and eight ways. Please help me or tell me a way that I can try to solve this problem.
Date: 07/28/2001 at 22:20:31 From: Doctor Peterson Subject: Re: Dividing regions of a square Hi, Pam. This problem is easier to solve than you would think. I suggest you start by thinking about wedge-shape pieces like this: s +---------------+ | | | | | | | + | | / \ | | / \ | | / \ | +---+-------+---+ a Then you can extend it to wedges that wrap around a corner like this: s +---------------+ | | | | | | | + | | / \ | | / + | / |b +---+-----------+ a You can find this area by drawing the line from the center to the corner to divide it into two triangles, and finding the area of each triangle. Once you've done this, I think you will have a good idea what to do. For a more detailed answer in our Dr. Math archives, see: Cutting a Square into Five Equal Pieces http://mathforum.org/dr.math/problems/shinichi.7.12.99.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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