Reference
In 1892 Alexander Gleason of Buffalo, New York was granted a patent for a "New Standard Map of the World", first published in 1889. The chart lays the entire surface of the Earth inside a single circle with the North Pole at its centre — the reason it has been reprinted and argued over continuously for more than a century.
Mathematically the chart is an azimuthal equidistant projection centred on the pole. Gleason's own patent describes it as a means of representing the globe on a flat sheet: distance measured outward from the centre is proportional to angular distance from the North Pole, and every meridian is a straight radius. The same projection is used today on the flag of the United Nations and by radio operators plotting great-circle bearings.
Because the geometry is exact, every latitude and longitude on Earth has one unambiguous position on the disc. That is what lets this site behave like a modern atlas: search a city and the marker lands on the spot the engraver intended.
The scan is normalised to a 1000 × 1000 square with the pole at its centre. For a point at latitude φ and longitude λ:
r = 2.61 × (90 − φ) x = 500 + r · cos(λ) y = 500 − r · sin(λ)
The equator therefore falls on a circle of radius 235 units, the Tropic of Capricorn sits well outside it, and Antarctica becomes the ice rim engraved around the edge. New York at 40.71° N, 74.01° W resolves to x 535.4, y 623.7.
Every flat map distorts something. On an azimuthal equidistant chart distances and bearings from the centre are true, while shapes and areas stretch progressively toward the rim — southern landmasses appear far wider than they measure on the ground. Read the disc as the historical instrument it is, and treat southern-hemisphere distances with that caveat in mind.