(Image: Freepik)
A prior post of this blog, Atomic Interstitial Sizes in Higher Dimensions, explored how the size of gaps between tightly packed spheres changes as one moves from two-dimensional to three-dimensional and on to higher dimensions.
Grant Sanderson, host of the 3Blue1Brown YouTube channel (I highly recommend following this channel), gave an exceptional lecture explaining how to calculate the volume of high-dimensional spheres. That lecture is: https://www.youtube.com/watch?v=fsLh-NYhOoU&t=3467s. While he doesn't directly speak about the interstitial sizes of the gaps found in my post, he does approach the problem by looking at the ratio of the sphere to cube volume in higher dimensions.
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