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

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Jan 13 02:24:08 PST 2004

```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

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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