Passing a Larger Cube Through a Smaller One
Date: 09/25/2003 at 11:47:26 From: Daryl Subject: spatial reasoning I've been told that, improbable though it may seem, it is possible to cut a hole through a solid cube so that a cube, larger than the original, can be passed in one end and out the other. How do you cut the hole?
Date: 09/25/2003 at 14:18:17 From: Doctor Douglas Subject: Re: spatial reasoning Hi Daryl, If you take a cube and look along the body diagonal (straight through from one corner to the opposite corner), you see the profile of a hexagon. You can put a square in this hexagon whose side length is greater than the original side length of the cube. This means that you can pass a larger cube completely through a smaller one. To verify this, you can draw a regular hexagon and try to maximize the area of a square that is inscribed within it. For directions on constructing a demonstration of this very interesting mathematical fact, check out the following page: Gabriel Nivasch -- Square Perforation on a Cube http://yucs.org/~gnivasch/cube/ Note that while the hexagon construction above does not give the _largest_ cube that can pass through another one. That cube is called Prince Rupert's Cube: Eric Weisstein's World of Mathematics -- Prince Rupert's Cube http://mathworld.wolfram.com/PrinceRupertsCube.html - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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