01 · Geography · 1,900 words
Colorado Is Not A Rectangle. It Has 697 Sides.
Congress drew four lines. Then men with compasses and metal chains went out to find them on the ground, and the ground won.
How many sides does Colorado have?
Colorado's boundary has 697 sides, not four. Congress defined the state as a rectangle between the 37th and 41st parallels and the 25th and 32nd meridians west of Washington, but the surveyors who marked the border on the ground in the 1870s and 1880s made hundreds of small errors, and the courts later ruled that the surveyed line — not the mathematical one — is the legal boundary. The technical term for a 697-sided polygon is a hexahectaenneacontakaiheptagon.
Every schoolchild in America learns that two states are rectangles: Colorado and Wyoming. It is one of those facts that feels too simple to be wrong.
It is wrong twice over.
Problem one: the Earth is round
Congress defined Colorado using lines of latitude and longitude — 37°N to 41°N, and 25°W to 32°W measured from Washington rather than Greenwich, which is how boundaries were written at the time.
That sounds like a rectangle. It is not, because lines of latitude run parallel and lines of longitude converge toward the poles. The eastern and western borders of Colorado are therefore slightly further apart in the south than in the north.
The practical consequence: Colorado's northern border is roughly 22 miles shorter than its southern border. Even in pure theory, before anyone picked up a surveying chain, the state was an isosceles trapezoid rather than a rectangle. The same is true of Wyoming.
Twenty-two miles is not a rounding error. It is the distance from downtown Denver to Boulder.
Problem two: the men with the chains
This is where it gets genuinely interesting, because there is a difference between two things that sound identical.
Delimitation is the description of a border — the words Congress writes down. Demarcation is going out into the physical world and putting stakes and stone cairns in the dirt to say here.
The official border is the demarcated one. Whatever the surveyors actually marked is what counts, not what Congress meant.
Colorado entered the Union in 1876. The first boundary survey team did not get around to translating that description into markers until 1879. Consider what those men were doing. No satellites. No GPS. Magnetic compasses and metal chains, walking a straight line across mountains, deserts and canyons, driving a marker every mile, in country with no roads.
They did remarkable work. They also made mistakes, constantly.
The Utah–Colorado survey is the clearest example. A single party started at the Four Corners in 1879 and marched north along what was supposed to be a fixed meridian, placing a marker each mile. When they reached the Wyoming line, they were not where they expected to be. Somewhere in that long walk, the line had jogged west. Later surveys in 1885 and 1893 found the errors — but by then the boundary was legally fixed at the original markers, and moving it would have required agreement from both states plus an act of Congress.
Nobody was going to do that. So the mistakes became the border.
The four big wobbles
Most of the 697 sides are tiny — a few dozen feet here, a hundred there. But there are several deviations big enough to see on a map if you know where to look.
The largest is on the western border, between the country near La Sal, Utah, and Montrose County near Paradox, Colorado. Over an eight-mile stretch, the survey team angled westward by more than a mile.
On the southern border with New Mexico there is a section known as the Edith Deviation, where the line bends to follow a small valley running northwest to southeast. That one may not be an error at all — it looks like the surveyors, for once, simply gave in to the terrain and followed the ground rather than fighting it.
And then there is the Oklahoma stretch. In the final 53 miles before the border turns north, along the flattest, most featureless country in the entire survey, the line swerves south by as much as 1,770 feet. There is no terrain to blame. The best guess anyone has offered is that the surveyors were confused by how completely featureless the place was.
The Supreme Court makes it permanent
Errors on the southern border with New Mexico eventually produced lawsuits, and those lawsuits climbed all the way to the U.S. Supreme Court.
In 1925 the Court ruled that the surveyed line was the real line. The mistakes were the border. They were not going to be corrected, then or ever.
That single decision is why the shape is permanent. Modern GPS can show you precisely where the mathematical border should be, down to the centimetre. It does not matter. The legal boundary is a set of nineteenth-century stone piles, and the law says the stone piles win.
The Four Corners is also in the wrong place
The most-photographed consequence of all this is the Four Corners Monument, the only point in the United States where four states meet.
It is not at the mathematically correct spot. The marker sits roughly 1,800 feet from where the meridian and parallel actually intersect.
People periodically discover this and get indignant about it, usually after driving several hours to stand on it. The courts have repeatedly and consistently ruled the same way they did in 1925: the surveyor's mark is the boundary. The monument is exactly where the corner legally is, because the corner is defined as being wherever the surveyor said it was.
Which is, if you think about it, a more honest way to run a country than pretending the map was ever perfect.
Why this is the best fact about Colorado
I like this story more than any other piece of Colorado trivia, and not because it is quirky.
It is the whole state in miniature. Colorado looks orderly from a distance — a clean box on a map, a tidy grid of counties, a rational plan. Get closer and it is all improvisation: people doing difficult work with inadequate tools in unforgiving country, making errors that then became permanent because undoing them was harder than living with them.
That describes the mining towns, the water law, the highway system and most of the ski industry too.
The state has 697 sides because a few dozen men walked across mountains and deserts with a compass and a chain and got it almost right. Almost right, permanently, is a very Colorado outcome.
And the word for a 697-sided polygon — hexahectaenneacontakaiheptagon — is real, is nearly unpronounceable, and is the single best thing you can drop into a conversation at a bar in this state.
Sources: U.S. Supreme Court boundary rulings (1925); Bureau of Land Management survey records; Denver Public Library Western History Collection; OpenStreetMap boundary data. The 697 figure counts distinct straight-line segments in the surveyed boundary.