Post #2712455
2026-02-28 14:44 UTC
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz
With a thin shell the slopes of the slicing surfaces are negligible.
With a thicker shell (outer diameter D and inner diameter d) such a surface should have a slope such that the outer edges have vertical distance D/n and the inner edges have vertical distance d/n. Thus a slicing surface is a part of a cone with its apex at the center of the spheres. This way the slices should have the same weight again.
Edit: Ok, I was too slow. You already wrote essentially the same.
Replies (1)
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@sibrosan@mastodon.social 2026-02-28 14:54
@hcschuetz@mastodon.social @divbyzero@mathstodon.xyz With a thick shell it's also negligible, it just depends on how much you are willing to neglect... Anyway, my point is that the claim that the weight/volume of any slice is the same, is simply not true, no matter how thin the shell.