Post #2712465
2026-03-01 14:48 UTC
@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.
Replies (1)
-
@hcschuetz@mastodon.social 2026-03-01 14:49
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz In more formal "Weierstraß style": For *whatever* relative difference ε > 0 we might be willing to neglect, there is a thickness δ > 0 such that |vol_planar - vol_conic| / vol_conic < ε for all shells with thickness δ or thinner, that is, for any r with R-δ <= r < R.