Mathematica(@mathemetica):A path can bend through space yet feel perfectly straight to an ant walking the surface. That turning inside the tangent plane is geodesic curvature k_g. When k_g = 0 the curve is a geodesic; the straightest possible route on S. Its space curvature k then satisfies k² = k_g² + k_n² Robot motion, mesh processing and relativistic orbits all compute these zero-k_g curves. Straightness is always measured against the geometry you inhabit.

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Mathematica@mathemetica

2026.08.26 17:50

A path can bend through space yet feel perfectly straight to an ant walking the surface. That turning inside the tangent plane is geodesic curvature k_g. When k_g = 0 the curve is a geodesic; the straightest possible route on S. Its space curvature k then satisfies k² = k_g² + k_n² Robot motion, mesh processing and relativistic orbits all compute these zero-k_g curves. Straightness is always measured against the geometry you inhabit.