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Last updated on April 24, 2014 at 17:35 EDT

Scientists Gain Insight into Aztec Arithmetic

April 4, 2008

Researchers say the ancient Aztecs maintained an arithmetic system that was far more complex than previously understood””using written symbols such as hearts, arrows and hands as alternatives to using fractions.

The researchers analyzed hundreds of drawings that were used to document agricultural properties by the Aztec people in the city-state of Tepetlaoztoc, near modern Mexico City. The manuscripts are dated between 1540 and 1544.

An examination of these hieroglyphic records showed that the Aztecs used their own calculation system to figure out things like the area of a parcel of land using symbols of hearts, hands, arrows, bones and arms.

The Aztecs have long been recognized for their sophistication in architecture, engineering, astronomy and other fields. And the new research confirms arithmetic can be added to the list.

“What we thought we knew about the Aztec measuring system was a little simplistic. We’ve determined that it was more complex,” said researcher Barbara Williams of the University of Wisconsin-Rock County said in a telephone interview.

Williams teamed with Maria del Carmen Jorge y Jorge of the Universidad Nacional Autonoma de Mexico.

The study was published in the journal Science.

“They used the four mathematical operations of addition, subtraction, multiplication and division. But in almost all of the early societies, they could do everything they needed to do, with just those four. They didn’t need square roots. They didn’t need trigonometry,” said Williams.

The two manuscripts were written on European paper by Aztecs a couple of decades after the conquest, using the Aztec system. One manuscript was found in a library in France and the other in Mexico.

Williams said they were land records drawn up that helped determine taxation imposed on the local people by the Spaniards.

“The fact that the Aztecs mathematically calculated areas has been known since 1980, but until now there was little understanding as to how they did it,” said Williams.

They Aztecs were a war-like people casually associated with human sacrifice””which they certainly performed, but they’re also known for their many accomplishments.

The new research adds further detail to the achievements of the Aztecs in other areas.

“This increases our understanding of Aztec culture. It gets to the idea that it was a numerate society in the rural areas as well as the urban areas — among the surveyors as well as the priests and the royalty,” said Williams.

The Aztec empire held sway over a large part of Mesoamerica for about a century until the arrival of the Spanish. Their capital Tenochtitlan””with towering pyramids and lavish architecture””was larger than any European city of the era.