Clairaut's theorem
From Wikipedia, the free encyclopedia
In mathematical analysis, Clairaut's theorem states that if
has continuous second partial derivatives at any given point in 
, say, 
then for 
In words, the partial derivatives of this function commute at that point. This theorem is named after the French mathematician Alexis Clairaut.
[edit] Clairaut's constant
A byproduct of this theorem is Clairaut's constant (alternatively known as "Clairaut's formula" and "Clairaut's parameter"), which relates the latitude, 
, and (here, spherical) azimuth, 
, of points on a sphere's great circle. The identification of a particular great circle equals its azimuth at the equator, or arc path, 
:
