![]() ![]() Around each of these corners draw a circle of radius 1. So it has corners at the points with Cartesian coordinates (+1, +1, +1, +1), (+1, +1, +1, -1), (+1, +1, -1, +1), (+1, +1, -1, -1), and you know what? Will you let me pretend we listed all sixteen corners? Thanks. But a four-dimensional hypercube, with each side of length 2 and centered on the origin. There is some largest sphere that you can draw, centered on the origin, the point with Cartesian coordinates (0, 0, 0), that just touches all of the corners’ circles. Around each of these eight corners draw a circle of radius 1. ![]() Draw a box with sides all of length two and centered on the origin. Now think of the three-dimensional analog. ![]() There is some largest circle that you can draw, centered on the origin, the dead center of the square, with Cartesian coordinates (0, 0), and that just touches all of the corners’ circles. Draw a square with sides of length two and centered on the origin. Start with a two-dimensional space, or as the hew-mons call it, a plane. I came across a little geometry thing that left me unsettled, even as I have to admit it’s correct. ![]()
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