I'd like to ask about sphere packing problem.
The question is: Pack three largest and identical sphere in a cube with a given length 1. Find the diameter of the sphere.
And can you kindly also draw the picture for me? I can't imagine that properly. Really thanks for your help.
2026-02-22 22:57:04.1771801024
Pack three largest sphere in a cube with given length.
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According to this paper, the optimal packing looks like this:
The spheres are of radius
$$r=\frac1{\sqrt2+2}\approx 0.2928932188134...\;.$$
And there is even space for a fourth sphere of the same size.