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Aztec arithmetic revisited: land-area algorithms and Acolhua congruence arithmetic
Barbara J Williams1, María del Carmen Jorge y Jorge
1Department of Geography and Geology, University of Wisconsin-Rock County, Janesville, WI 53546, USA.
Science (New York, N.Y.)
|April 5, 2008
Summary
Aztec land records reveal a unique indigenous calculation method. This "Acolhua congruence arithmetic" precisely determined agricultural field areas using proportions, not fractions.
Area of Science:
- Ethnomathematics
- Mesoamerican history
- Archaeology
Background:
- Aztec (Mexica) civilization utilized sophisticated land record systems.
- Understanding Aztec arithmetic and metrology is crucial for interpreting historical data.
Observation:
- Analysis of Acolhua-Aztec agricultural field records indicates discrepancies in calculated areas.
- Initial studies suggested indigenous calculation methods but couldn't fully explain all area values.
Findings:
- A significant percentage (60%) of recorded field areas were precisely reproducible using indigenous methods.
- A novel calculation system, termed "Acolhua congruence arithmetic," was identified, utilizing proportions and avoiding fractions.
- This method clarifies previously unexplained variations in Acolhua and Tenochca linear units.
Implications:
- The discovery of "Acolhua congruence arithmetic" enhances our understanding of Aztec mathematical practices.
- This finding provides new insights into Aztec metrology and record-keeping systems.
- It offers a framework for re-interpreting other historical land measurement data from the region.
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