Scientists find advanced geometry no secret to prehistoric architects in US Southwest

January 23, 2017
A satellite photo of Pueblo Bonito archaeological site with illustrations demonstrating its geometrical properties. Credit: Dr. Sherry Towers

Imagine you are about to plan and construct a building that involves several complicated geometrical shapes, but you aren't allowed to write down any numbers or notes as you do it. For most of us, this would be impossible.

Yet, new research from Arizona State University has revealed that the ancient Southwestern Pueblo people, who had no written language or written number system, were able to do just that - and used these skills to build sophisticated architectural complexes.

Dr. Sherry Towers, a professor with the ASU Simon A. Levin Mathematical, Computational and Modeling Sciences Center, uncovered these findings while spending several years studying the Sun Temple archaeological site in Mesa Verde National Park in Colorado, constructed around A.D. 1200.

"The site is known to have been an important focus of ceremony in the region for the ancestral Pueblo peoples, including solstice observations," Towers says. "My original interest in the site involved looking at whether it was used for observing stars as well."

However, as Towers delved deeper into the site's layout and architecture, interesting patterns began to emerge.

"I noticed in my site survey that the same measurements kept popping up over and over again," she says. "When I saw that the layout of the site's key features also involved many geometrical shapes, I decided to take a closer look."

A satellite photo of Sun Temple archaeological site with illustrations demonstrating its geometrical properties. Credit: Dr. Sherry Towers

The geometrical shapes used within this location would be familiar to any high school student: equilateral triangles, squares, 45-degree right triangles, Pythagorean triangles, and the "Golden rectangle," which was well known to architects in ancient Greece and Egypt and is often used in Western art due to its pleasing proportions.

With some geometrical know-how, a straight-edge, a compass or cord, and a unit of measurement, all of the shapes are fairly easy to construct. But, unlike the ancient Greeks, Egyptians and Maya, the ancestral Pueblo people had no written language or number system to aid them when they built the site. Incredibly, their measurements were still near-perfect, with a relative error of less than one percent.

"This is what I find especially amazing," Towers says. "The genius of the site's architects cannot be underestimated. If you asked someone today to try to reconstruct this site and achieve the same precision that they had using just a stick and a piece of cord, it's highly unlikely they'd be able to do it, especially if they couldn't write anything down as they were working."

During her research, Towers discovered that the site was laid out using a common unit of measurement just over 30 centimeters in length - equal to about one modern-day foot. She also found evidence that some of the same geometrical constructs from Sun Temple were used in at least one other ancestral Puebloan ceremonial site, Pueblo Bonito, located in New Mexico's Chaco Culture National Historic Park.

"Further study is needed to see if that site also has the same common unit of measurement," she says. "It's a task that will keep us busy for some years to come."

The study "Advanced geometrical constructs in a Pueblo ceremonial site, c. 1200 CE" will appear in the Journal of Archaeological Science: Reports.

Explore further: Ancient Chaco Canyon population likely relied on imported food

More information: S. Towers, Advanced geometrical constructs in a Pueblo ceremonial site, c 1200CE, Journal of Archaeological Science: Reports (2017). DOI: 10.1016/j.jasrep.2017.01.009

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nilbud
4.1 / 5 (9) Jan 23, 2017
There is no way she should be getting paid for this nonsense.
jeffreyjoemiller
1 / 5 (4) Jan 24, 2017
Eleanor Mannikka, a Trinity University academic, detailed similar research results re: Angkor Wat in her comprehensive book Angkor Wat: Time, Space, and Kingship.
katesisco
1 / 5 (2) Jan 24, 2017
Again and again we see phenomenal mathematical understanding that agrees with what has been published on this site in a previous article; that geometry seems to be 'built in' for humanity.
andyf
5 / 5 (4) Jan 24, 2017
Katesisco, I wouldn't deny we seem to be hard-wired for geometry but this article is a fine example of an author who has let Pareidolia overcome rational thought.

She states: "Incredibly, their measurements were still near-perfect, with a relative error of less than one percent".

Now just look at those lines she has drawn over the photographs and try and identify even one feature that meets that one percent claim.

Wishful thinking and Pareidolia.

If you look at it long enough, you'll notice there is a Flying Spaghetti Monster in one of the photographs.
antigoracle
3.7 / 5 (3) Jan 24, 2017
If you look at it long enough, you'll notice there is a Flying Spaghetti Monster in one of the photographs.

Whoaaa... was thinking that I was the only one.
DuhVinchE
5 / 5 (2) Jan 25, 2017
I have to admit that -- at least from the photo that is included in this article -- the structures look like they are quite haphazard, not the result of any mathematical precision. Perhaps the professor's full paper presents a more persuasive argument, but this just appears to be wishful thinking. The geometrical shapes overlayed over the picture above don't correspond at all to the shape of the actual structures.
cowabunga
not rated yet Jan 25, 2017
The author address the FSM siting in the paper.

"By mere random chance, any site may yield potential evidence of a
geometrical construct if enough site elements are examined, even
when no such constructs were actually used in the design of the site.
However, what makes this particular site unusual is the number of geometrical
constructs found when just a few site elements were considered.
And, most especially, the relationship of those geometric
constructs to the apparent common unit of measurement at the site is
extraordinarily unlikely to occur by mere random chance."
kamtravels2
not rated yet Jan 25, 2017
Actually those of us who have worked at and studied Chaco have known this for a long time. The structures are not haphazard and they have alignments to almost the nth degree. It is certainly okay that you might not believe it however we have worked there know she is correct in many ways.

Pueblo Bonito on it's axis is within 3 degrees of true north ...built with no compass. That's a fact.
bschott
not rated yet Jan 26, 2017
Actually those of us who have worked at and studied Chaco have known this for a long time. The structures are not haphazard and they have alignments to almost the nth degree. It is certainly okay that you might not believe it however we have worked there know she is correct in many ways.

Pueblo Bonito on it's axis is within 3 degrees of true north ...built with no compass. That's a fact.


I do not disagree with your assessment, to just up and build these structures without any means of planning other than verbal communication is very impressive, but what good is a compass for finding true north?
andyf
5 / 5 (2) Jan 26, 2017
kamtravels2 said:"Pueblo Bonito on it's axis is within 3 degrees of true north ...built with no compass."

Well, you don't need a compass. In fact a compass would just introduce an inaccuracy because magnetic north (mostly) doesn't align with true north.

All you need is Polaris to get true north to within 1 degree.

Straight lines are easily done by eye. Circles (and segments of) are easily done with a radial rope.

Similarly, you can use ropes for squares and rectangles.

Any three points constitute a triangle unless they lie in a straight line.

My point is not intended to denigrate the Puebloans building/planning skills - just to point out the author is seeing shapes in the clouds which don't even match up very well with the artifacts themselves.

There's more than one Flying Spaghetti Monster in there!

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