August epicycloidal projection
The August Epicycloidal projection is both a map and a decorative geometric experiment. Its outline, a nephroid (a two-cusped epicycloid), shows that cartography does not have to choose only between rectangles and ellipses.
A map that looks like a mathematical ornament
August Epicycloidal immediately draws attention through its shape. In a world dominated by rectangular maps, this form reminds us that flattening the globe is a design choice. The outline is not decoration; it explains how the spherical surface was translated onto a plane.
As a conformal projection, it can protect local angles, but its unusual form makes it difficult to use like an everyday atlas. It works best when you want to intrigue the viewer and show that map mathematics can be surprisingly plastic.
Global Cartographic Grid
Distortion Properties
| Property | Characteristic |
|---|---|
| Area | DistortedHighly distorted: scale increases rapidly away from the center, with the greatest enlargement toward the 180th meridian |
| Shape | PreservedPreserved locally (conformal, with no singular points) |
| Distances | DistortedHighly distorted |
| Angles and directions | PreservedPreserved locally (conformal) |
| Continuity | PreservedPreserved (the whole world fits inside a two-cusped epicycloid, a nephroid) |
History & Origin
Presented in 1874 by the German mathematician F. August (with G. Bellermann). It is a conformal projection (preserving angles) that fits the entire sphere inside a two-cusped epicycloid, or nephroid, with no part running off to infinity.
Applications
Mathematical cartography and decorative maps of aesthetic interest.
How to read this map
This is a map like an ornamental function plot: beautiful, logical, but requiring a slower reading pace.
- Notice the outline, because it reveals the projection's geometry.
- Local shapes can be convincing, but the global layout is unusual.
- It is best compared with other exotic projections.
- Do not use it for quick political relationship reading.
What you gain and lose
August protects local angles, but pays with an unusual outline and global distortions. It is visually attractive, but difficult for practical use.
Illustrations, cartographic history, and lessons about map geometry and aesthetics.
Political maps, first-contact education, and area comparisons.
Not sure this projection fits your map? Answer three questions in the finder →
Want to see it next to another projection? Compare: August Epicycloidal vs Mercator →
Can you recognize this projection without the label?
The projection quiz uses graticules and world outlines, so it is a natural next step from this page.
One attempt, the same set for everyone
Size illusion · Build a streak and come back tomorrow for another map.
✦ How do different countries look in this projection?
Analyze shape distortions of 5 countries in this cartographic projection and test them in the sandbox.
Brazil helps evaluate the tropics inside the unusual outline.
Test on map →
Australia shows what happens near the southern edge.
Test on map →
Russia tests continuity across large northern areas.
Test on map →
Greenland reveals how the projection treats polar regions.
Test on map →
Poland gives a familiar European reference point.
Test on map →Facts worth remembering
- The projection was created in the nineteenth century and still feels surprisingly modern.
- Its kidney-shaped outline, a nephroid, makes it easy to remember after one glance.
- It is a good example of map projection as an aesthetic decision.
Keep reading about maps that reshape intuition
Frequently Asked Questions
It is used for decorative map-making, collector atlases, and as an advanced mathematical display of conformal mapping.
It must not be used for measurement maps or school textbooks due to extreme scale inflation at the border lines.
Countries near the boundary curve (like New Zealand, Chukotka in eastern Russia, or Antarctica) which are giant-sized and highly warped.
Countries situated near the center (such as West African nations or Western and Central Europe). Scale changes most slowly there, so relative sizes are the most reliable.
It is conformal, meaning small shapes are preserved locally. However, because the whole world must fit inside a closed outline, scale grows rapidly toward its rim and regions at the edges undergo massive area enlargement.