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Aztec arithmetic: positional notation and area calculation.

H R Harvey, B J Williams

    Science (New York, N.Y.)
    |October 31, 1980
    PubMed
    Summary
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    The Aztec civilization utilized a sophisticated line-and-dot numerical system, including a zero and positional notation, for calculating agricultural field areas. This mathematical development rivals that of the Maya.

    Area of Science:

    • Mesoamerican Ethnomathematics
    • Archaeology
    • History of Mathematics

    Background:

    • The Texcocan-Aztec people of the Valley of Mexico employed diverse numerical notation systems.
    • Previous understanding often attributed advanced mathematical concepts like positional notation and the zero exclusively to the Maya civilization.

    Purpose of the Study:

    • To analyze the numerical system used in mid-16th-century Texcocan-Aztec land documents.
    • To determine if the Aztec numerical system incorporated concepts such as zero and positional notation.
    • To compare Aztec mathematical sophistication with that of other Mesoamerican cultures.

    Main Methods:

    • Decipherment of mid-16th-century native pictorial land documents from the Texcocan region.
    • Analysis of the line-and-dot numerical notation system for its structure and application.

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  • Examination of recorded agricultural field areas for evidence of arithmetic calculations.

    • Main Results:

    • The Texcocan-Aztec line-and-dot system included a symbol for zero.
    • Positional principles were used to assign values within the line-and-dot notation.
    • Evidence suggests areas of agricultural fields were calculated using arithmetic methods.

    Conclusions:

    • The Aztec numerical system featured both a zero and positional notation, challenging the notion of Maya uniqueness.
    • These findings indicate a highly developed mathematical system among the Aztecs, comparable to the Maya.
    • Ethnomathematical research continues to reveal the complexity of pre-Columbian American mathematics.