The Science of Cartographic Size Distortions
Representing a three-dimensional oblate spheroid on a flat, two-dimensional sheet of paper or screen mathematically requires compromise. Carl Friedrich Gauss proved in his Theorema Egregium (1828) that a spherical surface cannot be mapped to a plane without distortion of either area, angle, distance, or shape.
In 1569, Flemish cartographer Gerardus Mercator developed a conformal cylindrical projection specifically designed for marine navigation. Because it preserves angles and renders rhumb lines (lines of constant compass bearing) as straight lines, sailors could plot direct courses with a straightedge. However, to preserve angles, Mercator had to stretch the spacing between parallels of latitude by the secant of the latitude:
As a result, equatorial landmasses (like Africa, South America, and southern India) are depicted at their authentic scale (scale factor โ 1.0), whereas high-latitude landmasses like Greenland (72ยฐN, factor โ 10.5x), Alaska (64ยฐN, factor โ 5.2x), and Northern Europe (60ยฐN, factor โ 4.0x) are vastly exaggerated. Open Map Lab eliminates this bias by evaluating true ellipsoidal surface integrals on the WGS84 datum.