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A Square Problem (Posted on 2004-12-26) Difficulty: 4 of 5
Given a unit cube, what is the largest square that can be placed completely inside the cube?

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (5 votes)

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Problem Insight | Comment 11 of 17 |

Placing the base at the midpoints of the bottom base of the cube, the diagonal will be 2/2.  If you extend the side and tilt it so that the other base touches the midpoints of the top of the cube (also 2/2), you'll have a side that is 5/2.  Since this is not a square, you have to add a fixed number x to 2/2 and subtract the same fixed number from 5/2. So, (2/2 + x) = (5/2 - x), yielding x= (-2 + 5)/4.  Substituting x into one of our expressions, we reveal that the side of our square is:

(2 + 5)/4

A square with this side will be the largest square you can fit inside a unit cube.

  Posted by Marc Scapelitte on 2005-01-04 08:45:40
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