If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can find is just √2 - 1.(adsbygoogle = window.adsbygoogle || []).push({});

Doing a similar thing with a sphere in a cube we get √3 - 1

I've heard the n-dimensional analogue is √n - 1. Which is crazy as it means the gap is bigger than the radius of the sphere! (When n is greater than 4).

Anyway, how is such a thing proven?

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# The space between a unit 'sphere' in n dimensions within an n-dimensional cube

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