Advanced geometry used by prehistoric architects in US Southwest, say scientists

Posted: January 25, 2017 by oldbrew in History, Maths, Measurement, research
Tags: ,

[click on image to enlarge]

[click on image to enlarge]

Another one to add to the ‘how and why did they do that?’ list of ancient sites. Years of research lie ahead.

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, reports

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.”

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.

The report continues here.
[includes satellite photo of another site]

Tim adds


There are two sites. One of the builders must have known about the other.

37.165 -108.475


Seen from the site.

And the connection is?


  1. craigm350 says:

    Reblogged this on CraigM350 and commented:
    Just keeps popping up

  2. pyromancer76 says:

    If this is a quote, “the ancestral Pueblo people had no written language or number system to aid them when they built the site,” the authors might have been more humble (or scientific correct) and stated, “no known written language or number system.” How did their builders communicate with each other? Whatever symbols they might have used might have eroded away.

  3. hunter says:

    I ran across this particular mystery years ago. This last December I was able to visit the amazing site of Chichin Itza, in the Yucatan, and have visited the great huge pyramids outside of Mexico City twice. It is clear that the Maya and Aztec sites were organized deliberately to align with movement of the sun, moon and Venus. With this site, however, I wonder if the complex geometry was prospectively designed by the builders or is simply the way we can forensically analyze it from our perspective?

  4. carol says:

    Neolithic/ Bronze age people had a similar level of technology as the Pueblo but Alexander Thom was ridiculed for suggesting megalithic people used geometry to create ovoid stone circles and a standard unit of measurement. Okay for the politically correct friendly Pueblo but not for the nasty ancient people of Britain.

  5. jim says:

    Again, a but, just because there is no evidence of writing, does not mean it did not occur. You just may not have found it yet. But it’s settled science… OK, so does any group of Indians have a record source outside of “writing”, yes, oral tradition, if these scientists would improve their skill set, they would go back to the early French and English writings and notice the writing methods of many early nations. They used shells, and skins and other biodegradable communication methods. As memory aids, as story aids, which were land titles and important documents such as treaties. Where it was commonplace in the East and West of their territories, it may have been commonplace there and just have been overlooked. But to interpret, one would to have been there when it was committed to memory.

  6. oldbrew says:

    The abstract of their paper says:
    ‘These findings represent the first potential quantitative evidence of knowledge of advanced geometrical constructs in a prehistoric North American society, which is particularly remarkable given that the ancestral Pueblo peoples had no written language or number system.’

  7. oldbrew says:

    As Harry H mentioned in his link – and the report confirms – it’s quite easy to make a golden rectangle.

    Start with a square. Mark the midpoint of one side, and measure to one of the 2 opposite corners.
    Extend the line of the square from the midpoint to the length just measured.
    That’s the long side of the rectangle. The short side is the same length as each side of the square.

    In this diagram an arc is used, but you don’t need one because EB = EF.

    See ‘Drawing It’ here:

    Scaling it up to full size might be a bit more tricky, but probably not much of a problem for skilled people.
    Just a case of getting the measurements right.

    PS No number system needed – just measure out a square and mark halfway along one side and you’re in business.

    A triangle ECB would be a Conway triangle.

    Let DE = EC = 1
    DE + EF = 1 + √5 = DF
    DC = 2
    (1 + √5) / 2 = definition of Phi

    Ratio DC:DF = 1 : Phi
    That means ADFG must be a golden rectangle.

  8. tchannon says:

    I’ve added new content to the article which throws up some questions.

    You’ll need to use the aerial images, Google Earth or similar.

  9. oldmanK says:

    They could do a lot more than that. Not in 500bce but 5000bce.

  10. oldbrew says:

    According to the anthropologist Brian Fagan, “Pueblo Bonito is an archaeological icon, as famous as England’s Stonehenge, Mexico’s Teotihuacan, or Peru’s Machu Picchu.”

    ‘Next door’ is Chetro Ketl.

  11. Sphene says:

    Pueblo Bonita was contemporary with the Toltec civilization. The builders having access to advanced mathematical knowledge via Toltec traders would not be so unusual. Mesoamerican trade objects are known from Pueblo sites, as the Southwest was the source of turquoise.

  12. Sphene says:

    Is it too much of a stretch to consider that maybe the Mesa Verde and Pueblo Bonito communities “hired a contractor”, using contacts from the trade routes, to establish the important geometric boundaries and alignments for their building layouts?

  13. How long is a piece of string?

    That’s what you need; a piece of string. And some knots, if you like

  14. oldmanK says:

    Buildings based on the ‘golden ratio’ have aesthetic appeal, and so would be chosen simply for that and not for any mathematical construct/consideration. [the kitchen table I made myself to the golden ratio attracts attention for its proportions by people as dumb on the fact as the stray cats — ahem the cats prefer to sleep in an apple cardboard box 49.5cmx30cm=1.65]

    To be sure, intention of mathematical design has to be clear and definite. See this, one of several but i was not exact on date — its nearer 7000.

  15. Sphene says:

    From :

    “The Toltec empire established contact as far south as Central America, and as far north as the Anasazi corn culture in the Southwestern United States. The Toltec established a prosperous turquoise trade route with the northern civilization of Pueblo Bonito, in modern-day New Mexico. Toltec traders would trade prized bird feathers with Pueblo Bonito, while circulating all the finest wares that Mexico had to offer.. The Mayan city of Chichen Itza was also in contact with the Toltec civilization..”

    I agree that establishing geometric alignments is relatively easy with lengths of ropes (the Ancient Egyptians used ropes knotted in 3-4-5 lengths to establish right angles). It might have even been relatively easy to establish alignments over longer distances reflecting sunlight with pieces of shiny minerals. I just wonder how much the Pueblo peoples may have been influenced, and perhaps even assisted, by the Toltec traders. Trade is able to spread ideas and knowledge, and even people, quite far.