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2024-10-20 07:19:06

Greg Egan on Nostr: Here’s a fun puzzle for fans of the classical differential geometry of curves and ...

Here’s a fun puzzle for fans of the classical differential geometry of curves and surfaces.

Suppose a curve γ(s):R→R^3, parameterised by arc length s, is a geodesic on a surface of constant Gaussian curvature of –1.

Suppose γ''(s_0) = 0, but γ'''(s_0) ≠ 0.

What does that tells us about the torsion of γ(s) at s=s_0?
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