A sacred site built in southwest Colorado around 800 years ago hints that the ancestral Pueblo people might have used geometry, even though they lacked a written language or system of numerals, says a paper published in the April 2017 issue of Journal of Archaeological Science: Reports.
The analysis of the Sun Temple at Mesa Verde National Park offers the first hard evidence that a prehistoric North American society possibly employed such figures in construction.
Author Sherry Towers, a research professor with Arizona State University’s Simon A. Levin Mathematical, Computational and Modeling Sciences Center, knows that skeptics view such analyses — which are too often conducted by enthusiastic amateurs seeking everything from sacred geometry to ancient aliens — as bearing an “aura of quackery.” She was skeptical, too.
“It’s not just that I’m looking for shapes and, ‘Oh, look, there’s a square there.’ That’s not what led me to publish this," said Towers.
In fact, she didn’t set out to find geometrical figures at all. She was looking for astronomical alignments.
Many ancient peoples, including the one that built Mesa Verde’s several thousand ruins, erected structures that lined up with key solar and lunar cycles. It was while assessing the Sun Temple for such alignments that Towers encountered something odd: A repeating measurement of roughly 12 inches, or one third thereof.
“I was seeing similar measurements popping up over and over and over again in a way that was rather unlikely to occur by just mere random chance," Towers said.
A number of societies have used a similar unit of measure. Our modern imperial foot (12 inches) differs little from the Greek common foot (about 12.4 inches) and the Roman foot (about 11.6 inches).
Intrigued, Towers began looking at the design details of the oldest parts of the site. What she found surprised her.
“Not only did there seem to be a similar unit of measurement, but there also seemed to be some geometrical shapes that were key to how the site was laid out.”
Towers found signs that the ancestral Pueblo planned the Sun Temple using the golden rectangle, Pythagorean 3:4:5 triangles, equilateral triangles and 45-degree right triangles. A golden rectangle is one in which the ratio of the long side to the short side equals roughly 1:618.
This golden ratio crops up frequently in nature and corresponds to several interesting mathematical patterns. Architects have used it for millennia, and golden rectangles require only basic tools to construct.
Taken together, the repeated measurement and the geometric shapes would have been intriguing. Taken together, they gave Towers the confidence to publish.
“The probability that you would, just by mere random chance, find an equilateral triangle, and a square, and this golden rectangle, and all these different shapes in this thing — and then also have them involve this same repeated unit of measurement — is very low indeed.”
Towers explained that, though impressive, this rule-of-thumb geometry does not mean that these societies had what modern mathematicians would consider true geometry or advanced mathematics.
“You can do geometry without knowledge of algebra," Towers said.
The ancestral Pueblo settled Mesa Verde around 470 A.D. and occupied the area until drought drove them out in the late 1200s.
