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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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re(2): Where To Place The Square | Comment 8 of 17 |
(In reply to re: Where To Place The Square by Jer)

Viewed from above, one slanted edge of the tilted square cuts off on the base of the cube the hypotenuse of a right triangle that is 1/4, 1/4 and sqrt(2)/4, that last being the hypotenuse, and the length of the projection of a side of the square onto the base.  Since the top of the side is on the top of the cube, it is 1 unit up.  The angle that the side (and therefore the plane of the square) makes with the vertical is therefore arcsin(sqrt(2)/4) = 20.7048... degrees, making the square have an angle of 69.295... degrees with the horizontal base.

The angle of an edge of the square with a vertical face of the cube would have a sine equal to (1/4)/sqrt(1+1/4^2), making the angle 14.036... degrees.  But this is not the angle between the planes.

 

 


  Posted by Charlie on 2004-12-27 02:13:30
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