Mathematical accuracy of Aztec land surveys assessed from records in the Codex Vergara

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 108; no. 37; pp. 15053 - 15057
• Main Authors: Jorge, María del Carmen, Williams, Barbara J, Garza-Hume, C. E, Olvera, Arturo
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 13-09-2011; National Acad Sciences
• Subjects: Accuracy; Agricultural land; Agriculture; Ancient Lands; Approximation; Arithmetic; Aztec culture; Circles; Comparative analysis; Coordinate systems; Data Collection; Error rates; Ethnic Groups; Humans; Land surveying; Mathematics; mathematics and statistics; Measurement; Mexico; Models, Theoretical; Physical Sciences; Polygons; Records as Topic; Social Sciences; Vertices; Ancient Lands; Mexico
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1107737108

Land surveying in ancient states is documented not only for Eurasia but also for the Americas, amply attested by two Acolhua–Aztec pictorial manuscripts from the Valley of Mexico. The Codex Vergara and the Códice de Santa María Asunción consist of hundreds of drawings of agricultural fields that uniquely record surface areas as well as perimeter measurements. A previous study of the Codex Vergara examines how Acolhua–Aztecs determined field area by reconstructing their calculation procedures. Here we evaluate the accuracy of their area values using modern mathematics. The findings verify the overall mathematical validity of the codex records. Three-quarters of the areas are within 5% of the maximum possible value, and 85% are within 10%, which compares well with reported errors by Western surveyors that postdate Aztec–Acolhua work by several centuries.