the following hieroglyph
represent a mapping . It is enough to take
to G.P.S -ing (almost) every point in which are at distance one from the origin. That is the sphere.
Now the partial derivatives and are pictorially as:
These derivative are:
An easy calculation give that for the inner products , so the are orthogonal to the position . Then the product , which is orthogonal to the plane determined by the couple of vectors , hence colinear to the position . In fact, after normalization .
A good exercise is to unfold the same program for the torus by employing the parameterization given by: