Rectangular States

Strictly speaking, they're not rectangular but trapezoidal. Their borders are defined in terms of lines of latitude and longitude; but this means that they're slightly narrower in the north than in the south, because lines of longitude converge as you move away from the equator. The difference for Colorado is about 21 miles.

In fact it's not even as simple as that, because of the curvature of the Earth's surface. If you look at an outline map of the US states, for example here on Wikipedia, you'll see that the line that forms the southern border of Utah, Colorado and Kansas is even curved on the map.

If we were being really pedantic, we could say because they're on a convex surface and not a flat one, they aren't even two–dimensional.

In short: Goodness knows what shapes they are in reality. I certainly don't, and I couldn't find anywhere on the Internet that does; so I'm happy to think of them as rectangular.

There's more information on the Mathematical Tourist blog.

The only US state apart from Colorado and Wyoming that has only 'straight' borders is Utah, which would be as rectangular as those two if it hadn't lost its north–east corner to the latter of them.

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