Post #2712453

2026-02-28 14:02 UTC

@divbyzero@mathstodon.xyz If you did it with the dimensions I suggested, you would find that the slice from the middle weighed much more than the slice from the top. In your case (with a much thinner shell) the difference might be small enough to dismiss as measurement error, but if accurately printed and weighed it will be there.

Replies (2)

@divbyzero@mathstodon.xyz 2026-02-28 14:29

@sibrosan@mastodon.social Ah! I misuderstood your original comment. I thought you just wanted me to make the model larger. You are 100% correct. In fact, this is version 2.0. For version 1.0, the sphere was smaller with the same thickness walls, and when I sliced the sphere straight across, the difference in weight was measurable. So, in this version 2.0, I made the sphere larger and the slices are sliced along cones converging at the origin rather than along flat planes. That way, the "height" of each radial shell in the thin solid object is the same. (It has the added benefit that one ring sits slightly inside its neighbor, which is nice.)

Open ##2712454
@hcschuetz@mastodon.social 2026-02-28 14:44

@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.

Open ##2712455