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### Cutting Cake with Geometry

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Date: 2/4/96 at 4:37:18
From: Mittledorf Joshua J
Subject: Geometry puzzle

Here's a cute geometry puzzle that came to me from a very public
source, which I'm too embarrassed to credit:

A cake is square when viewed from the top.  Height is unspecified.
It is iced on top and the four vertical sides.  How can the cake be
divided in 5 pieces such that each piece has the same amount of cake and
the same amount of icing?  How can you minimize the number of cuts you
have to make in the cake and still meet this target?  Alternatively, how
can you minimize the total length of the cuts you make in the cake?

- Josh Mitteldorf
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```
Date: 2/12/96 at 12:46:37
From: Doctor Ken
Subject: Re: Geometry puzzle

Hello -

You listen to Car Talk too?

When I heard this puzzle on National Public Radio, I thought of this
solution: the cake has a certain perimeter whn viewed from the top.  Let
the perimeter be called "P."  Then find five points around the perimeter
such that they divide the perimeter into five equal parts (each with the
same length, in other words).  Now if you cut the cake into five
pieces, and make sure that the corners of the pieces are these five
points and the tops of the five pieces have the same surface area, then
you'll have done it!

The other parts of the puzzle can be gotten by drawing pictures and
messing around with them: for example, you know it's going to take at
_least_ three cuts, because two cuts can only get you four pieces.

-Doctor Ken,  The Math Forum

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Associated Topics:
High School Geometry
High School Polyhedra
High School Practical Geometry

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