Aztec Math Used Hearts and Arrows

By David Biello

AZTEC MATH: The Aztec used symbols such as arrows and hearts to denote fractional units of measurement in surveying records like the Oztoticpac Lands Map pictured here.
COURTESY OF LIBRARY OF CONGRESS

The Aztecs had more numbers than we do, or at least symbols denoting numerical concepts. When it came to measuring land—critical for levying the proper tax or tribute—these medieval Mesoamericans used arrows, hearts, hands and other units representing fractions, according to a new study in Science.

To figure this out, mathematician Maria del Carmen Jorge y Jorge of the National Autonomous University of Mexico (U.N.A.M) channeled the mind of an Aztec land surveyor. That meant retraining herself to use a different numerical system and combing through the Codex Vergara, one of two remaining books that record Aztec land surveying.

Working with geographer Barbara Williams and del Carmen Jorge y Jorge counted 367 fields in this book with both an overall area for the plot of land as well as the lengths of the sides. Roughly 60 percent of these fields had areas that matched the basic mathematical rule of length multiplied by width or other common surveying calculations.

But the rest were off, usually by a small amount. And 69 had areas that were prime numbers such as 211—numbers that cannot be created by multiplying two whole numbers together, such as 20 times 10. Instead, del Carmen Jorge y Jorge determined that the Aztecs were using the equivalent of fractions.

Read the rest on Scientific American.