August epicycloidal world map: how country sizes change

August epicycloidal projection: key facts and what it does to country sizes

Distortion class

Conformal

Graticule type

Epicycloidal

Creator

F. August and G. Bellermann

Year

1874

Area

Highly distorted: scale increases rapidly away from the center, with the greatest enlargement toward the 180th meridian

Shape

Preserved locally (conformal, with no singular points)

Distances

Highly distorted

Angles and directions

Preserved locally (conformal)

The August epicycloidal projection is conformal and has no singular points, so all the Tissot indicatrices are circles, none of them cut. They differ only in size, and by a lot. The smallest lie near the middle of the map, on the equator at 30° longitude: their area is only 7% larger than at the central point in the Gulf of Guinea. The largest sit in the corners of the grid, at 60° latitude and 150° longitude, where area grows more than thirteenfold and the circle's diameter more than three and a half times. The whole world fits inside one closed outline, and both poles sit in sharp notches in the middle of its top and bottom edges.

Unlike Mercator, enlargement here depends on longitude as well as latitude. On the equator the circle at 90° longitude has 1.9 times the area, and the one at 150° already 6.4 times. The area isocoles form arcs and ovals around the middle of the map: the 2× line crosses the prime meridian at about 52.5°, the 4× line at 69.5°, and at 150° longitude the 8× line already begins at 35°. The angular isocoles stay empty.

Poland, at 52°N and 19°E, has its area roughly doubled here. Drag it to the middle of the map and it shrinks to half its current size, keeping its shape. Move it east to around Kamchatka at the same latitude and it grows more than fivefold. New Zealand, at the very edge of the map, is enlarged about sixteen times, so this striking map is no good for comparing the sizes of countries.