Cutting Cake with GeometryDate: 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 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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