Within the fields of Geometry and mechanics, a displacement is a vector, the length of which is the shortest distance from an initial, to a final position of some point $P$ in Motion.

Historically, it has not always been that Mathematics was respected, or even trusted. In fact, some of the people responsible for laying the foundations of Christian doctrine were known to have said "bewareMathematicians", and the Roman legal authorities labeled Geometry and Mathematics in general damned, and forbidden.

Geometry

While mathematics can not be cleanly defined, it can be broken up into roughly three sectors: Algebra, Geometry, and Mathematical Analysis.

Geometry