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.
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
