Post #2712458
2026-02-28 15:35 UTC
@hcschuetz@mastodon.social @divbyzero@mathstodon.xyz
I don´t doubt that you can adjust the inner shape of the slices to get them the exact same volume. Whether the cone cut, as you describe, does that, i'm not so sure. You're a mathematician, right? Can you prove it?
Replies (1)
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@hcschuetz@mastodon.social 2026-02-28 22:35
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz Well, I'm not a mathematician, but I can prove it. I don't know into how much detail a proof must go to convince you, but here is an attempt: We have a shell delimited by an outer sphere with radius R and an inner sphere with radius r. The spheres have the same center C. (In your example R = 150 mm and r = 1 mm, but we need not restrict ourselves to these values.) 1. Select some piece P of the outer sphere.