Colorado is a rectangle? Think again.

The Centennial State has 697 sides‚ not four.

  • 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…

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.

Four Corners (and four more)

Four Corners. Clockwise from top left: Utah, Colorado, New Mexico, Arizona. Image source: Getty Creative

Located in a dusty, desolate corner of the desert, the Four Corners monument seems very far from the middle of anything. Yet this is the meeting point of four states: Utah, Colorado, New Mexico and Arizona. It is the only quadripoint in the United States (4). The monument's exact location is at 36°59'56″N, 109°02'43″W.

However, it's not where Congress had decreed the four states to meet. That point is about 560 feet (170 m) northwest of the quadripoint's current location, at 37°N, 109°02'48″W. Did you drive all the way through the desert to miss the actual point by a few hundred feet?

No, you didn't: in 1925, the Supreme Court ruled that the borders as surveyed were the correct ones. But perhaps the original quadripoint deserves a small marker of its own, if only to provide the site with an extra attraction. Or why not go for three? Some sources say the original point deviates by 1,807 feet (551 m).

 The La Sal/Paradox deviation

Paradox Valley in Colorado, near the (crooked) border with Utah. Image source: Wikimedia Commons/Tony Webster, CC BY 2.0


In 1879, a survey party marched north from Four Corners, placing markers at every mile. The surveyors eventually reached the Wyoming border, but not where they thought they'd end up. Later surveys, in 1885 and 1893, found out where the original surveyors had gone wrong, but by that time the border as surveyed had become the official one. Changing it would have required both Colorado and Utah to agree on a solution, and Congress to approve it.

The biggest error occurs just south of the road connecting La Sal, Utah to Paradox, Colorado. Across an eight-mile stretch, the surveyors strayed westward before regaining true north. The resulting deviation is 3860 feet (1.18 km).

Things go south after Edith

I

Border deviation near Edith, CO. Image source: Google Maps/Ruland Kolen

West to east, Colorado's border with New Mexico starts out fairly straight. However, just east of Edith, the border swerves southeast for about 3,400 feet (1 km) before resuming its course due east, now 2,820 feet (860 m) further south than before.

Why? It seems that for once, the surveyors have given in to the dictates of topography: the deviation follows a small valley oriented northwest-southeast.

Panhandling into Oklahoma

The Colorado border swerves south, eating into the Oklahoma Panhandle. Image source: FascinatingMaps.com

Almost at the end of their surveying mission, it seems the party lost the plot again. In the last 53 miles (85 km) before the border turns north, the stretch where Colorado rubs against Oklahoma, the line again swerves to the south, by as much as 1,770 feet (540 m).

Don't blame the terrain: appropriately for a place so close to the Oklahoma Panhandle, it's as flat as a pancake. Perhaps the surveyors were confused by the very featurelessness of the place.

Colorado is a 697-sider

Each dot is a twist in Colorado's supposedly straight borders. Image source: FascinatingMaps.com

These are just four of the biggest, most easily spotted surveying errors. In total, Colorado's borders have hundreds twists and turns — most much smaller than the Big Four. Here they are: every dot on is a border deviation, as indicated on the OpenStreetMap of Colorado.

Accordingly, the state has not just four sides, but a total of 697 sides. So if Colorado is not a rectangle, what is it? Well, not a pentagon, (Greek for 5-sider), hexagon (6-sider) or a heptagon (7-sider), but a — hold on to something — hexahectaenneacontakaiheptagon (697-sider).

Don't get your hopes up, Wyoming

Wyoming: just as fallible as Colorado — but more willing to admit its mistakes. Image source: FascinatingMaps.com

With Colorado thoroughly disqualified to as one of America's two truly rectangular states, does that leave Wyoming holding the crown all on its own? Nope. Turns out the surveyors who plotted the Equality State's outline were just as fallible as the Colorado set.

This map shows a few larger ones of the many deviations in on all four sides of Wyoming. Interestingly, the deviations shown come in pairs, whereby the second ones seem to correct the deviation of the first ones.

So, while Wyoming is just as imperfect as Colorado, it does seem that at least it is better at admitting (and correcting) its mistakes than its southern neighbor.

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.

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Politics & Current Affairs

Political division is nothing new. Throughout American history there have been numerous flare ups in which the political arena was more than just tense but incideniary. In a letter addressed to William Hamilton in 1800, Thomas Jefferson once lamented about how an emotional fervor had swept over the populace in regards to a certain political issue at the time. It disturbed him greatly to see how these political issues seemed to seep into every area of life and even affect people's interpersonal relationships. At one point in the letter he states:

"I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend."

Today, we Americans find ourselves in a similar situation, with our political environment even more splintered due to a number of factors. The advent of mass digital media, siloed identity-driven political groups, and a societal lack of understanding of basic discursive fundamentals all contribute to the problem.

Civil discourse has fallen to an all time low.

The question that the American populace needs to ask itself now is: how do we fix it?


Discursive fundamentals need to be taught to preserve free expression

In a 2017 Free Speech and Tolerance Survey by Cato, it was found that 71% of Americans believe that political correctness had silenced important discussions necessary to our society. Many have pointed to draconian university policies regarding political correctness as a contributing factor to this phenomenon.

It's a great irony that, colleges, once true bastions of free-speech, counterculture and progressiveness, have now devolved into reactionary tribal politics.

Many years ago, one could count on the fact that universities would be the first places where you could espouse and debate any controversial idea without consequence. The decline of staple subjects that deal with the wisdom of the ancients, historical reference points, and civic discourse could be to blame for this exaggerated partisanship boiling on campuses.

Young people seeking an education are given a disservice when fed biased ideology, even if such ideology is presented with the best of intentions. Politics are but one small sliver for society and the human condition at large. Universities would do well to instead teach the principles of healthy discourse and engagement across the ideological spectrum.

The fundamentals of logic, debate and the rich artistic heritage of western civilization need to be the central focus of an education. They help to create a well-rounded citizen that can deal with controversial political issues.

It has been found that in the abstract, college students generally support and endorse the first amendment, but there's a catch when it comes to actually practicing it. This was explored in a Gallup survey titled: Free Expression on Campus: What college students think about First amendment issues.

In their findings the authors state:

"The vast majority say free speech is important to democracy and favor an open learning environment that promotes the airing of a wide variety of ideas. However, the actions of some students in recent years — from milder actions such as claiming to be threatened by messages written in chalk promoting Trump's candidacy to the most extreme acts of engaging in violence to stop attempted speeches — raise issues of just how committed college students are to
upholding First Amendment ideals.

Most college students do not condone more aggressive actions to squelch speech, like violence and shouting down speakers, although there are some who do. However, students do support many policies or actions that place limits on speech, including free speech zones, speech codes and campus prohibitions on hate speech, suggesting that their commitment to free speech has limits. As one example, barely a majority think handing out literature on controversial issues is "always acceptable."

With this in mind, the problems seen on college campuses are also being seen on a whole through other pockets of society and regular everyday civic discourse. Look no further than the dreaded and cliche prospect of political discussion at Thanksgiving dinner.

Talking politics at Thanksgiving dinner

As a result of this increased tribalization of views, it's becoming increasingly more difficult to engage in polite conversation with people possessing opposing viewpoints. The authors of a recent Hidden Tribes study broke down the political "tribes" in which many find themselves in:

  • Progressive Activists: younger, highly engaged, secular, cosmopolitan, angry.
  • Traditional Liberals: older, retired, open to compromise, rational, cautious.
  • Passive Liberals: unhappy, insecure, distrustful, disillusioned.
  • Politically Disengaged: young, low income, distrustful, detached, patriotic, conspiratorial
  • Moderates: engaged, civic-minded, middle-of-the-road, pessimistic, Protestant.
  • Traditional Conservatives: religious, middle class, patriotic, moralistic.
  • Devoted Conservatives: white, retired, highly engaged, uncompromising,
    Patriotic.

Understanding these different viewpoints and the hidden tribes we may belong to will be essential in having conversations with those we disagree with. This might just come to a head when it's Thanksgiving and you have a mix of many different personalities, ages, and viewpoints.

It's interesting to note the authors found that:

"Tribe membership shows strong reliability in predicting views across different political topics."

You'll find that depending on what group you identify with, that nearly 100 percent of the time you'll believe in the same way the rest of your group constituents do.

Here are some statistics on differing viewpoints according to political party:

  • 51% of staunch liberals say it's "morally acceptable" to punch Nazis.
  • 53% of Republicans favor stripping U.S. citizenship from people who burn the American flag.
  • 51% of Democrats support a law that requires Americans use transgender people's preferred gender pronouns.
  • 65% of Republicans say NFL players should be fired if they refuse to stand for the anthem.
  • 58% of Democrats say employers should punish employees for offensive Facebook posts.
  • 47% of Republicans favor bans on building new mosques.

Understanding the fact that tribal membership indicates what you believe, can help you return to the fundamentals for proper political engagement

Here are some guidelines for civic discourse that might come in handy:

  • Avoid logical fallacies. Essentially at the core, a logical fallacy is anything that detracts from the debate and seeks to attack the person rather than the idea and stray from the topic at hand.
  • Practice inclusion and listen to who you're speaking to.
  • Have the idea that there is nothing out of bounds for inquiry or conversation once you get down to an even stronger or new perspective of whatever you were discussing.
  • Keep in mind the maxim of : Do not listen with the intent to reply. But with the intent to understand.
  • We're not trying to proselytize nor shout others down with our rhetoric, but come to understand one another again.
  • If we're tied too closely to some in-group we no longer become an individual but a clone of someone else's ideology.

Civic discourse in the divisive age

Debate and civic discourse is inherently messy. Add into the mix an ignorance of history, rabid politicization and debased political discourse, you can see that it will be very difficult in mending this discursive staple of a functional civilization.

There is still hope that this great divide can be mended, because it has to be. The Hidden Tribes authors at one point state:

"In the era of social media and partisan news outlets, America's differences have become
dangerously tribal, fueled by a culture of outrage and taking offense. For the combatants,
the other side can no longer be tolerated, and no price is too high to defeat them.
These tensions are poisoning personal relationships, consuming our politics and
putting our democracy in peril.


Once a country has become tribalized, debates about contested issues from
immigration and trade to economic management, climate change and national security,
become shaped by larger tribal identities. Policy debate gives way to tribal conflicts.
Polarization and tribalism are self-reinforcing and will likely continue to accelerate.
The work of rebuilding our fragmented society needs to start now. It extends from
re-connecting people across the lines of division in local communities all the way to
building a renewed sense of national identity: a bigger story of us."

We need to start teaching people how to approach subjects from less of an emotional or baseless educational bias or identity, especially in the event that the subject matter could be construed to be controversial or uncomfortable.

This will be the beginning of a new era of understanding, inclusion and the defeat of regressive philosophies that threaten the core of our nation and civilization.