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?
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?