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Science 4 April 2008:
Vol. 320. no. 5872, pp. 72 - 77
DOI: 10.1126/science.1153976
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Research Articles

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

Barbara J. Williams1 and María del Carmen Jorge y Jorge2*

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.

1 Department of Geography and Geology, University of Wisconsin–Rock County, Janesville, WI 53546, USA.
2 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, FENOMEC, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México D.F., Mexico.

* To whom correspondence should be addressed. E-mail: mcj{at}mym.iimas.unam.mx

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Science. ISSN 0036-8075 (print), 1095-9203 (online)