Mathematics of the Incas

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.

[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.

[2] One of the main references confirming this are the chronicles that present a hierarchy of organized authorities, using the decimal numeral system with its arithmometer: Quipu.

This can be appreciated in the following table:[note 2] The quipus constituted a mnemonic system based on knotted strings used to record all kinds of quantitative or qualitative information; if they were dealing with the results of mathematical operations, only those previously performed on the "Inca abacuss" or yupanas were cancelled.

[11] In October 2010, Peruvian researcher Andrés Chirinos with the support of the Spanish Agency for International Development Cooperation (in Spanish, Agencia Española de Cooperación Internacional para el Desarrollo, AECID), reviewed drawings and ancient descriptions of the indigenous chronicler Guaman Poma de Ayala and finally deciphered the riddle of the yupana — that he calls "pre-Hispanic calculator" — as being capable of adding, subtracting, multiplying, and dividing.

Every hatun runa or "common man" received a plot of land upon marriage and its production had to satisfy the basic needs of food and trade of the spouses.

Among these measures of capacity there is the poctoy or purash (almozada), which is equivalent to the portion of grains or flour that can be kept in the concavity formed with the hands together.

[16] The ancient inhabitants of the Andes knew the scales of saucers and nets as well as the huipe, an instrument similar to steelyards.

[17] Apparently, its presence is associated with the works of jewelry and metallurgy, trades in which it is necessary to know the exact weights to use the right proportions of the alloys.

Especially the volume of their colcas (trojas) and their tambos (state warehouses, located in key points of the Qhapaq Ñan).

Months, years, and the phases of the moon — much consulted for the tasks of sowing, aporques and harvests and in navigation — were also measured in days.