Peirce quincuncial projection

The Peirce quincuncial projection is a conformal map projection developed by Charles Sanders Peirce in 1879.

History

The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane. While working at the U.S. Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879 (Peirce 1879), having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a polygon of n sides (known as the Schwarz–Christoffel mapping). In the normal aspect, Peirce's projection presents the Northern Hemisphere in a square; the Southern Hemisphere is split into four isosceles triangles symmetrically surrounding the first one, akin to star-like projections. In effect, the whole map is a square, inspiring Peirce to call his projection quincuncial, after the arrangement of five items in a quincunx.

After Peirce presented his projection, two other cartographers developed similar projections of the hemisphere (or the whole sphere, after a suitable rearrangement) on a square: Guyou in 1887 and Adams in 1925. The three projections are transversal versions of each other (see related projections below).