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Frenet-Serret formulas

For a unit-speed curve on the unit sphere,
$$
\alpha=-\kappa^{-1}n-\tau^{-1}\kappa^{-2}\dot\kappa\,b,
\qquad
\kappa_g=-\kappa^{-1}\tau^{-1}\dot\kappa
$$
under the compatible signed-torsion and geodesic-curvature conventions.


Curvature decomposition for a spherical curve

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 26J / a / Solution

Curvature decomposition for a spherical curve

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Curvature decomposition for a spherical curve

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