Coordinate Systems

Abstract

In this chapter we revise Cartesian coordinates, axial systems, the distance between two points in space, and the area of simple 2D shapes. It also covers polar, spherical polar and cylindrical coordinate systems. René Descartes is often credited with the invention of the xy-plane, but the French lawyer and mathematician Pierre de Fermat (1601–1665) was probably the first inventor. In 1636 Fermat was working on a treatise titled Ad locus planos et solidos isagoge, which outlined what we now call “analytic geometry”. Unfortunately, Fermat never published his treatise, although he shared his ideas with other mathematicians such as Blaise Pascal (1623–1662). At the same time, Descartes devised his own system of analytic geometry and in 1637 published his results in the prestigious journal Géométrie. In the eyes of the scientific world, the publication date of a technical paper determines when a new idea or invention is released into the public domain. Consequently, ever since this publication Descartes has been associated with the xy-plane, which is why it is called the Cartesian plane.