One truth, many shapes

Equal-area means a region's size on the map matches its size on the ground, wherever it sits. It says nothing about shape. Mollweide's ellipse, the Gall-Peters rectangle from the last chapter, Equal Earth's rounded outline and Goode's homolosine below are all, mathematically, equally honest about size, and look almost nothing alike.

Karl Mollweide published his ellipse in 1805: longitude lines curving gently from a straight equator to two poles that are each a single point. It never caught on for general maps, shapes feel cramped near its corners, but the maths became the foundation several later projections, Goode's included, are built on.

In 1923 J. Paul Goode combined two projections into one: a sinusoidal band near the equator, where shapes stay closest to true, flanked by Mollweide above and below. He then went further still and cut the whole map open over the oceans, into separate lobes, so no single piece had to stretch as far to stay equal-area. The result looks torn apart. That is deliberate: it is the price of keeping every remaining piece closer to its true shape.