Homolosine — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
The land would move Goode's lobes before his join
Goode chose his lobes by eye: where the cuts run and where each lobe's meridian sits. Scored on the land outside Antarctica and found exactly on a five-degree grid, the land's own layout at his count of two lobes north and four south deforms it by 14.48° against his 16.51° — two degrees, more than his meridians were worth in the first place — while its cuts cross less land than his: 2,057 kilometres against 2,391, the worst of them 1,056 against the 1,946 his northern cut spends on Greenland. The land wants the map's edge in the Atlantic and its northern cut in the Pacific. His fourth southern lobe is worth four hundredths of a degree, and once the lobes are the land's the best join climbs again, to sixty degrees.
The ocean centres its lobes on the land's cuts, and cannot keep its own cuts short
Run on the water instead of the land, the same exact search gives an interrupted homolosine whose lobes sit on the Pacific, the Atlantic and the Indian Ocean — five of its six central meridians within twenty degrees of a cut the land's own layout chose — and it deforms the water by 13.31° against the 19.75° the land's layout gives it. The inversion stops at the cuts. Every meridian on Earth crosses at least 7,172 kilometres of water, so the ocean's map has no layout whose cuts stay under seven thousand, where the land's went below nine hundred. And no layout serves both: none comes within 2.57° of both optima at once, though a single wide Pacific lobe buys the water 2.8° for a tenth of a degree of land.
The water would join Goode's map at seventy-five degrees
Goode joined the sinusoidal to the Mollweide at 40° 44′, and the land, given its own lobes, moves that join up to sixty degrees. The water moves it further, to seventy-five, and gains twice as much by it — a full degree of mean angular deformation against the land's half — though less of the northern water than of the northern land lies above Goode's join. The gain is in the polar water, north and south, where Goode's Mollweide cap shears even the lobes' own meridians; the water just above his join, the northern edge of the Southern Ocean among it, pays part of it back. A separate join for each hemisphere is worth a few hundredths of a degree, and with the join free the one-layout-for-both question comes out the same way it did with the join fixed, only worse: no layout comes within 3.3 degrees of both surfaces' best at once.
Named alongside it
The objects these essays reach for when they reach for this one.
Angular deformationCentral meridianEqual-areaInterruptionVerificationCut lengthPareto frontTrade-offLobeMollweideSeamSinusoidal