A high-dimensional sphere spilling out of a high-dimensional cube
Is there some obvious way (that I seem to be missing) to see that the centrally inscribed D-sphere <i>must</i> touch all of the other spheres in high dimensions?<p>That's probably a stupid question, but while that fact is intuitively obvious for D={2,3} -- as this problem tries to demonstrate -- higher dimensions are unintuitively WEIRD.