Colorado is a rectangle? Think again.

• Colorado looks like a rectangle. It isn't.
• The Centennial State has not four, but 697 sides. That makes it a hexahectaenneacontakaiheptagon.
• Does that make Wyoming the only real rectangular state? Well, about that…

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America loves its straight-line borders. The only U.S. state without one is Hawaii – for obvious reasons (1).

West of the Mississippi, states are bigger, emptier and boxier than back East. From a distance, all seem to be made up of straight lines.

Only when you zoom in do you see their squiggly bits: the northeast corner of Kansas, for instance. Or Montana's western border with Idaho that looks like a human face. Or Oklahoma's southern border with Texas, meandering as it follows the Red River.

New Mexico comes tantalisingly close to having only straight-line borders. There's that short stretch north of El Paso that would have been just 15 miles (24 km) long if it was straight instead of wavy.

No, there are only three states whose borders are entirely made up of straight lines: Utah, which would have been a rectangle if Wyoming hadn't bitten a chunk out of its northeastern corner; Wyoming itself; plus Colorado.

Red: states with only straight-line borders. Yellow: states with some straight-line borders. Green: states without straight-line borders.Image: mapchart.net

Except that they aren't. For two distinct reasons: because the earth is round, and because those 19th-century surveyors laying out state borders made mistakes.

Congress defined the borders of Colorado as a geospherical rectangle, stretching from 37°N to 41°N latitude, and from 25°W to 32°W longitude (2). While lines of latitude run in parallel circles that don't meet, lines of longitude converge at the poles.

Which means that Colorado's longitudinal borders are slightly further apart in the south. So if you'd look closely enough, the state resembles an isosceles trapezoid (3) rather than a rectangle. Consequently, the state's northern borderline is about 22 miles (35 km) shorter than its southern one. The same goes, mutatis mutandis, for Wyoming.

That's not where the story ends. There's boundary delimitation: the theoretical description of a border, as described above. But what's more relevant is boundary demarcation: surveying and marking out the border on the ground. Colorado entered the Union in 1876.

Only in 1879 did the first boundary survey team get around to translating Congress's abstract into actual boundary markers. The official border would not be the delimited one, but the demarcated one. Unfortunately, 19th-century surveyors lacked satellites and other high-precision measurement tools.

Let's not be too harsh: considering the size of the task and the limitation of their tools — magnetic compasses and metal chains — they did an incredible job. They had to stake straight lines irrespective of terrain, often through inhospitable land.

But yes, errors were made — and were in fact quite habitual. Take for example the 49th parallel, which for more than 1,200 miles forms the international border between the U.S. and Canada. Rather than being a straight line, it zigzags between the 912 boundary monuments established by successive teams of surveyors (the last ones in 1872–4). The markers deviate by as much as 575 feet north and 784 feet south of the actual parallel line.

Colorado, not as rectangular as you think. Image: FascinatingMaps.com

The same kind of thing happened when the first surveying teams went out to demarcate the Colorado border. This map magnifies four of the most egregious surveying inaccuracies, where the difference between the boundaries delineated by Congress and the border demarcated by the surveyors is greatest.

Maps of Colorado and Wyoming both by FascinatingMaps.com.

Strange Maps #945

Got a strange map? Let me know at strangemaps@gmail.com.

(1) If you're not into the whole obviousness thing: Hawaii is a bunch of islands, which therefore don't have a land border — neither with other U.S. states or third countries.

(2) That's west of the Washington Meridian — the third one, to be exact. Over time, four Washington meridians were defined as prime meridians for the U.S. They passed through the Capitol, the White House, the Old Naval Observatory and the New Naval Observatory. Defined by Congress in 1850 at 77°2'48.0"W of Greenwich, the third Washington meridian was used as the base line for a number of western state borders, including:

• at 17°W, a stretch of border with Texas in the west, and Arkansas and Louisiana in the east. This line passes through the two-state conurbation of Texarkana;
• at 25°W, the Colorado-Kansas border (and part of the Nebraska-Colorado border);
• at 26°W, a stretch of the border between Texas and New Mexico (the Oklahoma-New Mexico border, just to the north, is set back two miles to the east);
• at 27°W, the 555-mile stretch from Colorado north to the Canadian border, separating Montana and Wyoming in the west from the Dakotas and Nebraska in the east;
• at 32°W, the straight line from Wyoming to Mexico, separating Utah and Arizona in the west from Colorado and New Mexico in the east (also running through Four Corners, where these four states meet).

Defined from the now standard Greenwich Meridian, the eastern and western extremities of Colorado are 102°2'48"W to 109°2'48"W, respectively

(3) An isosceles trapezoid is a four-sided shape with two parallel sides and two non-parallel but equal sides.

(4) The only state-level quadripoint. There are, in fact, dozens of quadripoints between U.S. counties, hundreds between U.S. municipalities, and indeed thousands (of usually bilateral ones) on the edges of checkerboard-patterned Indian reservations and other federally reserved territories.