Geodesic curvature measures how much a curve bends or turns. For example, a straight line has geodesic curvature zero at all of its points. The absolute value of the geodesic curvature of a circle is the same for all its points too and depends only on the circle's radius. A large radius means that the circle is almost straight and so the curvature is small. But a small radius means that the bending is fast and so the curvature is large. The sign of geodesic curvature depends on the direction of the curve. If we are traveling in a circle counterclockwise, the curvature is positive. But if we move in the opposite direction, the curvature is negative.

Suppose we want to find the geodesic curvature of a curve called c at a point called p. First draw the tangent line to the curve at c. One...