The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.
Jacobi's Curvature Theorem
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Cite this as:
Weisstein, Eric W. "Jacobi's Curvature Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JacobisCurvatureTheorem.html