Circle and square problem
Date: Around 1995
Take a circle and place it in the center or four others. It is obvious that
it is contained in a square. It is obvious if we go to 3-d the sphere in
the center, r will be contained in a cube. In 4-d, the hypersphere is
contained in the hypercube. This is not obvious, but true. My question is
whether or not this containment continues for dimensions higher than 4.
Well, I am not sure you have really clarified. Mostly, you seem to have
repeated what you said before. But maybe we can work it out together. Let
us start with the 2-d case: Give the coordinates of the center of each of
your circles, and their respective radii. Then give the coordinates of the
corners of the square that you say "includes" them so I will know your
definition of "include". Then we can go on from there and see what the
difficulties are in the higher dimensions.
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Update: June 2012