Circle and square problem ```Name: yendor Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1995 ``` Question: 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. Replies: 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. jlu Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs