In higher dimensions most of the volume of a n-sphere is found close to its shell.
The volume of such a sphere is Vn(R)∝Rn. [1]
The ratio of the volume of a shell to the rest of the ball is
Vn(R+Δ)−Vn(R)Vn(R)=(1+ΔR)n−1
which grows quickly with n.
The embedding places the tokens in areas where there is the most space to accommodate them.
[1] https://en.wikipedia.org/wiki/Volume_of_an_n-ball
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In higher dimensions most of the volume of a n-sphere is found close to its shell.
The volume of such a sphere is Vn(R)∝Rn. [1]
The ratio of the volume of a shell to the rest of the ball is
Vn(R+Δ)−Vn(R)Vn(R)=(1+ΔR)n−1
which grows quickly with n.
The embedding places the tokens in areas where there is the most space to accommodate them.
[1] https://en.wikipedia.org/wiki/Volume_of_an_n-ball