Math Forum - Project of the Month

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December 1998 Project of the Month

Inscribing Nice Boxes in Nice Spheres

December's Winners

This problem came to me after seeing a picture like the one above on my co-worker Ron's screen. I got to thinking, and he and I got to talking, and this is what came out of it.

The picture above is of a box inscribed in a sphere (trust me). Here's the question: For all spheres up to 15 units in diameter, find the dimensions of all the boxes with integer edges that can be inscribed in a sphere with a diameter that is also an integer.

Make sure that you know exactly what it means for a box to be inscribed in a sphere. Feel free to mention anything interesting that you notice as you go along.

(Solutions should be submitted anytime by the end of the first week of January - take the holiday vacation to work on it!)

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