Exotic Projections: Peirce, Berghaus and beyond
Explore unusual projections: Peirce quincuncial, the Berghaus star, August epicycloidal and the orthographic globe. Flattening the world differently.
Beyond the cylinder and the cone
A world map usually brings to mind a rectangle, as with Mercator, or an ellipse, as with Mollweide. Mathematics allows many other ways to flatten the globe, though. Cartographers and mathematicians have designed maps shaped like a square, a star or a kidney-like curve. They look unusual today, but each shows that distortion can be placed deliberately.
The Peirce projection: the world in a square
The projection was presented in 1879 by Charles Sanders Peirce, the American philosopher and mathematician, who was then working for the U.S. Coast and Geodetic Survey. The Northern Hemisphere fills the middle of a square, and the Southern Hemisphere is split into four parts in the corners. Hence the name “quincuncial”, after the Latin pattern of five points.
Which projection inflates areas near the poles the most?
The projection is conformal except at four points on the Equator, where this property fails. According to the USGS album of map projections, it was the first use of elliptic functions to build a map. Learn more in the Peirce projection guide.
Other geometric curiosities
- Berghaus star: presented in 1879 by the German Hermann Berghaus. The Northern Hemisphere is shown in an azimuthal equidistant projection, and the Southern Hemisphere is divided into five triangular arms. The map was used in the logo of the Association of American Geographers. Details: Berghaus projection.
- August epicycloidal: a conformal projection presented in 1874 by F. August and G. Bellermann. The whole world fits inside a curve with two cusps, called an epicycloid. In 1942 Athelstan Spilhaus used an oblique form of it for a map of the world's oceans. Details: August projection.
- Orthographic projection: a perspective projection in which the Earth is seen as if from an infinite distance. It shows at most one hemisphere at a time, but it looks like a globe. It was already known in antiquity. Details: orthographic projection.
Why do we need unusual maps?
These projections are not meant for car navigation or flight planning. The USGS album describes the Peirce and August maps as novelty world maps. They still have real educational value: they show that every map chooses where to hide its distortion. See how these projections change the shapes of countries on the interactive map.