Ernie--
You mentioned the advantage of a conformal projection, which correctly reproduces angles.
But though the gnomonic isn't conformal, districts that result from rectangles on a gnomoniic are practically indistinguishable from rectangular. Their corners differ from a right angle only by a tiny amount.
Even if the entire U.S. were mapped with the gnomonic projection, centered at the center of the country, a district, at one extreme end of the country, at the periphery of the map, a district which is square on the gnomonic map will, on the ground, have corners that only differ from right angles by about 1.4 degrees. That's if the district has one of its corners pointed toward the center of the map. If the district has one of its _sides_ pointed toward the center of the map, and if it has the average area that national senate districts would have if the senate had districts, then it's corners will differ from a right angle by only a fraction of a degree.
And if, instead of a national map, it's a state map, even for a state with great extent, like California, the districts' corners will only differ from a right angle by a fraction of a degree, regardless of how they're oriented with respect to the center of the map.
So, to have districts whose corners don't differ perceptibly from a right angle, it isn't necessary to use a conformal projection or a cylindirical projection.
Districts whose boundaries are latitude/longitude llines will have corners that are exactly right angles.
The longitude lines, meridians, are straight lines on the ground. The latitude lines, parallels, are circles on the ground--constant curvature. If you were driving a road along a parallel, you'd have the steering wheel at a constant position to drive along the parallel.
Longitude/latitude district lines, the geographical earth co-ordinate system, is an appealing way to make rectanglar districts.
The all-straight district lines made by rectangles on a gnomonic projection are appealing too
Previously I'd said that the gnomonic would give noticibly unsquare districts when a country as big as the U.S. is mapped. Not so. I'd initially believed that because I'd seen gnomonic maps showing nearly half of the world, and maps of such a large area can have great area exaggeration and shape distortion at the periphery, especially for large shapes. But that isn't true of the gnomonic when it's mapping a country. Well of course a country as large as Russia would have somewhat more departure from rectangularness than the U.S. would.
Mike Ossipoff
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