Research Article

Aztec Arithmetic Revisited: Land-Area Algorithms and Acolhua Congruence Arithmetic

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Science  04 Apr 2008:
Vol. 320, Issue 5872, pp. 72-77
DOI: 10.1126/science.1153976

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Acolhua-Aztec land records depicting areas and side dimensions of agricultural fields provide insight into Aztec arithmetic. Hypothesizing that recorded areas resulted from indigenous calculation, in a study of sample quadrilateral fields we found that 60% of the area values could be reproduced exactly by computation. In remaining cases, discrepancies between computed and recorded areas were consistently small, suggesting use of an unknown indigenous arithmetic. In revisiting the research, we discovered evidence for the use of congruence principles, based on proportions between the standard linear Acolhua measure and their units of shorter length. This procedure substitutes for computation with fractions and is labeled “Acolhua congruence arithmetic.” The findings also clarify variance between Acolhua and Tenochca linear units, long an issue in understanding Aztec metrology.

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