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> cone

For physical tiles, clearly not as the curvature would be wrong. I'm sure there remain interesting questions, but it's not sufficiently obvious to me what projection makes sense that I'm able to get further into the problem.

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I now realized I wanted to say cylinder, not cone haha.

That's also interesting!

Assuming it's possible at all, I think scale winds up mattering in a way that it doesn't for a plane, because you have to accommodate "meeting yourself" again some fixed distance away.

A cone has the same curvature as the plane.

Not for any definition of curvature that springs to mind. There may well be definitions for which that's true (let me know, I'm curious!), but they're not what I meant. As I said, I was considering covering a cone with physical tiles. My point was that the same tile cannot be placed at different heights along the cone, because a slice along the tile will have to conform to ever larger circles.

The Gaussian curvature is the same. That is the curvature that can be measured "from within" the surface.

What you wrote is of course right as well

Ah hah, neat!

How do you define the curvature for a cone when it has a singularity at the apex? From the definion that I know (angle defect), the tip of the cone will have curvature

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