I propose a stacked combination of 3 Cylindrical Equal-Area world-maps.
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Cylindrical Equal-Area (CEA) maps have big advantages, and the disadvantage that each of them has really bad shapes at some latitudes. And the ones with good tropical shapes have relatively great NS compression and relatively small min-scale at high-lat.
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CEA has the advantage of being the 2nd simplest equal-area map. (Sinusoidal is the simplest, but people don't like its shape-distortions and small min-scale.) ...and the easiest one for which to draw the grid, because the grid consists of all straight-lines.
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Also, Cylindrical projections are able to give information, via the special ruler about which I've posted here, that other maps can't give.
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Different CEA versions differ in their aspect-ratio (ratio of EW/NS dimensions). Each version looks good at some latitudes.
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e.g. Behrmann shows the tropics with acceptable shapes, without too much flattening or loss of min-scale at high-lat.
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Tobler CEA is a square map, with equal NS and EW dimensions. (Its aspect-ratio is 1.0). Tobler has the advantage that, even up to Norway's arctic coast (North-Cape), the min-scale is no less than the scale along the equator. But the price for that is that tropical regions are hugely shape-distorted, with Aftrica and South-America looking even more implausiblly-skinny than in Peters. (...not that it could really get any more implausible than that.)
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And, in that way, Tobler also wastes lots of space to distort the tropics.
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Well, Tobler is good for high-lat, and Behrmann is good for low-lat. So then, why not use Tobler only where needed?
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Behrmann's min-scale is no less than the scale along the equator, up to lat 41.41 That's approximately the latitude of Mount Shasta and Barcelona, Spain.
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So why not map the entire Earth on Behrmann, and have, directly above it, on the page or map-sheet, a Tobler map showing the Earth from lat 41.41 to the North Pole?
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In fact, though this is less needed south of the equator, because the inhabited land doesn't reach as far toward the pole, you could do the same thing in the South. From minus 41.41 to the South Pole, have a map on which the min-scale at Cape-Horn is no less than the scale along the equator. That would be a CEA map whose aspect-ratio, if it mapped the whole Earth, would be about 1.8
That's 1.743 times less than that of Lambert's CEA map, and about 1.31 times Behrmann's aspect-ratio.
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This stack of 3 maps would have an overall aspect-ratio of 1.45. It would neatly fit on an 8.5X11 sheet of paper, with a little space left over at top and bottom in the 8.5-inch dimension.
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...and it would show every part of the Earth, from Cape-Horn to North-Cape, with local min-scale no less than the scale along the equator, and with acceptable shape.
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I doubt that there's any other non-interrupted equal-area world-map for which that can be said.
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I call that map "CEA-Stack".
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Michael Ossipoff
May 1st, 2020