Monday, March 16, 2020

[tqakkdbc] Which cylindrical equal-area map projection for Boston schools?

Boston, Massachusetts has dictated that the Peters map projection (Gall-Peters) be the only map projection permitted to be purchased for world maps in Boston public schools.  (Something something reparations for slavery.)

Unlike Mercator, cylindrical equal-area map projections such as Gall-Peters are not conformal.  (No equal area map projection can be conformal, though I don't know a proof.)  North-south scale equals east-west scale only along one parallel (line of latitude), the standard parallel, for each hemisphere.

Gall-Peters chooses that standard parallel to be at 45 degrees.  Boston missed an opportunity to dictate a better standard parallel, for example, 42 degrees 21 minutes, a parallel that passes through the middle of the city.  That would keep areas around Boston as least distorted in shape as possible, because learning accurate local geography is practically important for students.  (Though it's pretty hard to see features in and around Boston on world map unless you have a huge map.)

In contrast, the 45 degree N line of latitude is the Vermont-Canada border, an inaccessible frozen wasteland in the far, far north.

Incidentally, in choosing a projection that keeps regions around 45 degrees latitude minimally distorted, namely most of Europe, it could be argued Gall-Peters perpetuates the same issues of European dominance and importance, continuing legacies of its colonial power, that Peters accused Mercator of doing.  It's OK if the shapes of shithole countries are distorted, so long as the shapes of European countries are accurate.

Demonstrate distortion by zooming in on a satellite image of a baseball diamond (which should be square) in an area far from the standard parallel.  This requires a Gall-Peters projection satellite image viewer; I don't know where to find such a thing.  I think Google Maps uses Mercator (Web Mercator), which is (roughly) conformal.

The Lambert cylindrical equal area projection puts the standard parallel at the equator, so regions near the equator have the least distortion.  That probably shows the least favoritism, though I'm sure some identity politics argument could also be cooked up disparaging it.

Practically, an equal area map projection remains equal area even if stretched or shrunk horizontally or vertically, so simply choose an aspect ratio (implicitly choosing a standard parallel) that matches the printable area of the paper onto which you are printing the map, or the constraints of the space you have to display it.

No comments :