Quipukamayuq with his quipu and a yupana, the main instruments used by the Incas in mathematics.
The mathematics of the Incas (or of the Tawantinsuyu) was the set of numerical and geometric knowledge and instruments developed and used in the nation of the Incas before the arrival of the Spaniards. It can be mainly characterized by its usefulness in the economic field. The quipus and yupanas are proof of the importance of arithmetic in Inca state administration. This was embodied in a simple but effective arithmetic, for accounting purposes, based on the decimal numeral system; they too had a concept of zero,[1] and mastered addition, subtraction, multiplication, and division. The mathematics of the Incas had an eminently applicative character to tasks of management, statistics, and measurement that was far from the Euclidean outline of mathematics as a deductive corpus, since it was suitable and useful for the needs of a centralized administration.[note 1]
On the other hand, the construction of roads, canals and monuments, as well as the layout of cities and fortresses, required the development of practical geometry, which was indispensable for the measurement of lengths and surfaces, in addition to architectural design. At the same time, they developed important measurement systems for length and volume, which took parts of the human body as reference. In addition, they used appropriate objects or actions that allowed to appreciate the result in another way, but relevant and effective.
^Ascher M. and Ascher R. (1985). "El quipu como lenguaje visible". In Heather Lechtman, Ana María Soldi (ed.). La tecnología en el mundo andino (in Spanish). Vol. 1. Mexico City: UNAM. ISBN 9789688372937.
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