Post #2712464
2026-03-01 14:47 UTC
@sibrosan@mastodon.social
Good that we agree on the conic cuts now. But sorry, I can't resist to discuss the words "wrong" and "negligible" a bit.
I wouldn't call @divbyzero@mathstodon.xyz's initial statement "wrong". The conic cutting can be seen as a less interesting detail not worth mentioning in that context. (It might even have confused some readers.)
But yes, it can be misunderstood easily if one implicitly transfers the planes from Archimedes' statement on 2D surfaces to the 3D shells.
Replies (2)
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@hcschuetz@mastodon.social 2026-03-01 14:48
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz And when I called the cut slopes "negligible" for thin shells, this was not about a particular amount or percentage of difference I'm willing to neglect, but it was an informal/sloppy way to say that the difference between planar and conic cuts decreases faster than linearly if we make the shell thinner. So even the relative difference approaches zero by making the shell sufficiently thin.
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@sibrosan@mastodon.social 2026-03-01 16:03
@hcschuetz@mastodon.social @divbyzero@mathstodon.xyz The statement plainly claimed the slices would have the same volume, no limits on shell thickness, no "approximately". That is demonstrably not true.