Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry. The formula relates the distance r(t) from a point on a great circle

Great circle

A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

 of the unit sphere

Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point...

 to the z-axis, and the angle θ(t) between the tangent vector and the latitudinal circle:


The relation remains valid for a geodesic on an arbitrary surface of revolution

Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve around a straight line in its plane ....

.