Mathematics
Curvature of Space Curves and the Frenet–Serret Formulas
Quick fact
For any smooth curve in space, at each point there exists a unique orthonormal frame—the Frenet–Serret frame—whose motion along the curve is completely determined by just two numbers: curvature (how much it bends) and torsion (how much it twists).
Why this is interesting
You know how a straight line has no curvature, but how do we measure how much a curve twists through space? There is a clever set of formulas that tells us exactly how any space curve bends and twists at every point.