Monday 2 September 2013

A Quincuncial Projection of the Sphere

The Quincuncial projection of the sphere is a way of projecting what is on the surface of a sphere (like the surface of the Earth) onto a square, or more accurately onto a tessellation of squares. 

It was invented in 1879 by the American polymath and measurement scientists Charles Sanders Peirce. His illustration of the projection is shown below.According to Peirce, his projection has the following properties:

1. The whole sphere is presented on repeating squares.
2. The part where the exaggeration of scale amounts to double that at the centre is only 9% of the area of the sphere, against 13% for Mercator's projection and 50% for the stereographic.
3. The angles are exactly preserved.
4. The curvature of lines representing great circles is, in every case, very slight, over the greater part of their length.

In addition it can be tessellated in all directions.
Image from HERE.