Mercator's rhumb lines: a multivariable application of arc length

Gerardus Mercator's map-projection technique of the 16th century can be used to solve the calculus problem of multivariable arc length. Mercator's map enabled rhumb lines, which are constant bearing paths connecting two points. These rhumb lines can be parametrized using rectangular coordinates and trigonometric identities. An improper integral then gives arc length in real three-dimensional space.