Why the United Nations flag and ballistic missile maps share the same geometry

Countries & Cities · Published 30 September 2026 Swipe more like this →

In short: The azimuthal equidistant projection is a unique map style that keeps distances and directions perfectly accurate from a single chosen center point. While it is a practical tool for radio operators and military strategists, its ability to distort the globe has also made it a favorite for modern conspiracy theorists.

At its core, the azimuthal equidistant projection acts as an exponential map on a sphere. By selecting a specific point—defined by latitude and longitude—as the center, the projection ensures that every other location on the map remains at a proportionally correct distance and azimuth from that origin. This makes it an invaluable utility for point-to-point communication, as radio operators can center the map on their own antenna to determine the exact bearing needed to reach a distant transmitter.

The projection’s history is surprisingly deep. While some suggest ancient Egyptian origins in religious texts, the first formal description appears in an 11th-century work by al-Biruni. By the 1500s, it was already in use by Spanish and Portuguese navigators to visualize the territorial boundaries established by the 1494 Treaty of Tordesillas. Later, prominent cartographers like Gerardus Mercator and Guillaume Postel—the latter giving the projection its French and Russian name—employed it for polar regions and star charts.

Despite its utility, the projection has inherent limitations. Because it represents a sphere on a flat plane, distortion increases as one moves away from the center. Distortions are minimal within 10,000 km, moderate up to 15,000 km, and severe beyond that. If a map is extended to its maximum radius of 20,000 km—half the Earth's circumference—the point antipodal to the center smears into a massive circle. This effect is why a map centered on Taipei severely distorts South America, while one centered on Los Angeles remains relatively clear.

In the 21st century, the projection has found an unlikely second life. Because it depicts the Earth as a circular plane with the North Pole at the center and Antarctica as a surrounding ring, it has been adopted by Flat Earthers as a definitive map of their worldview. This interpretation often leans on the UN flag, which uses a polar azimuthal equidistant projection to represent the globe.

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