[EM] 2 minor corrections about U.S. districts

[MIKE OSSIPOFF]

When I spoke of a gnomonic map of the U.S., I meant a map of the 48 
contiguous states.

It wouldn't be practical to map the contiguous states, Alaska & Hawaii all 
on the same gnomonic map, for drawing the rectangular districts. Anyway, of 
course as it's done now, each state has its own district map.  If the most 
distant parts of those 3 regions are 180 degrees apart, then it would be 
impossible to map them all on the same gnomoniic map anyway.

Another minor error:

Where I said "1.4 degrees", that should have been 2.8 degrees. I was looking 
at half of the angle.

So:

If congressional districts were made by drawing rectangles on a gnomonic map 
of the contiguous 48 states then, if a square district had a size equal to 
the average size that senate districts would have if the senate had 
districts, and if that square district were at one extreme end of the 
contiguous states, at the periphery of the map, then that square's corners 
could, at most differ from right angles by 2.8 degrees. That's about 1/20 of 
a radian.

I'd previously said 1.4 degrees. I was looking at half of the angle.

That's if one corner of the square is pointing at the center of the map. 
That's the orientation for maximum distortion of the square's corners. If 
the square has a side facing the map's center, then, as before, the corners 
differ from right angles by only a fraction of a degree.

And, as before, if it's a California map instead of a contiguous states map, 
the square's corners will differ from right angles by only a fraction of a 
degree, regardless of how the square is oriented with respect to the center 
of the map.

I having suggested drawing rectangles on a gnomonic map, it's of interest 
how much the resulting districts on the ground could depart from 
rectangularness. Very little, it turns out.

Of course, for a large oblong area, a district at an extreme end of that 
area would more  nearly have a side towards the center of the map rather 
than a corner.

Mike Ossipoff

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