Peirce's Quincuncial Projection
While working at the U.S. Coast and Geodetic Survey, the American philosopher (actually polymath) Charles Sanders Peirce disclosed his projection in 1879, having been inspired by H.A. Schwarz's 1869 conformal transformation of a circle onto a polygon of n sides. In the normal aspect, Peirce's projection presents the northern hemisphere in a square; the other hemisphere is split into four 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 cross.
About the man:
Charles Sanders Peirce (pronounced purse), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. Although Peirce was educated as a chemist and was employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or semiotics, that he is largely appreciated today. The philosopher Paul Weiss, writing in the Dictionary of American Biography for 1934, called Peirce "the most original and versatile of American philosophers and America's greatest logician" (Brent, 1).
Peirce was largely ignored during his lifetime, and the secondary literature was scant until after World War II. Much of his huge output is still unpublished. Although he wrote mostly in English, he published some popular articles in French as well. An innovator in fields such as mathematics, research methodology, the philosophy of science, epistemology, and metaphysics, he considered himself a logician first and foremost. While he made major contributions to formal logic, "logic" for him encompassed much of what is now called the philosophy of science and epistemology. He, in turn, saw logic as a branch of semiotics, of which he is a founder. In 1886, he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later to produce digital computers.