Incan mathematics is a general term that refers to the understanding and use of numbers and geometry and development of such tools by Incan civilizations, previous to the arrival of the Spanish. Namely, the Incans used this knowledge for economic applications and developed a mathematical system especially useful for a centralized administration.[1] The "quipu" and the "yupana" were important tools that demonstrate the importance of mathematics in the management of their civilization. They were able to create a simple, yet effective decimal-based system which was especially useful for accounting. Incan mathematicians understood the number zero[2] and utilized addition, subtraction, multiplication, and division for management, statistical and measurement tasks.
Creation of roads, canals, and monuments such as fortress and city layouts required a practical geometric system with measurements for length, surfaces, and other aspects of architectural design. They developed systems for length and volume by using the human body for reference.
Counting Systems
edit| Ordered As | Number of Families |
|---|---|
| Puriq | 1 family |
| Pisqa kamayuq | 5 families |
| Chunka kamayuq | 10 families |
| Pisqa chunka kamayuq | 50 families |
The dominant counting structure followed a base-decimal system[3]. Evidence of this is supported by the use of the Incan creation of a Quipu, whose use was discovered in chronicles that showed a hierarchy of organized authorities. This is also confirmed by the interpretation of the elements of the Quipu, which contained knots organized according to location to represent units like tens, hundreds, etc[4]. The main confirmation, however, is through the expression in the denomination of the numbers in Quechua, in which the numbers are developed in a decimal way (as shown in the table below). (The Quechua used below is from Cuzco).
| Number | Quechua | Number | Quechua | Number | Quechua |
|---|---|---|---|---|---|
| 1 | Huk | 11 | Chunka hukniyuq | 10 | Chunka |
| 2 | Iskay | 12 | Chunka iskayniyuq | 20 | Iskay chunka |
| 3 | Kimsa | 13 | Chunka kimsayuq | 30 | Kimsa chunka |
| 4 | Tawa | 14 | Chunka tawayuq | 40 | Tawa chunka |
| 5 | Pisqa | 15 | Chunka pisqayuq | 50 | Pisqa chunka |
| 6 | Suqta | 16 | Chunka suqtayuq | 60 | Suqta chunka |
Quipus
editPrincipal Article: Quipus
The Quipu consisted of a mnemonic system based on knotted cords through which both quantitative and qualitative information were recorded. Mathematical records were kept also on the yupana as well. The Quipu was also an instrument useful for accounting, census information, product amounts, and values for state deposits. There have even been mentions of its use as a way to record traditions and history, of course in a method much different from writings.
Other writings also mention the quipus as a way to keep historical news, but details of the system have not been discovered. Specialized personnel known as the quipucamayoc handled the ropes and were able to take charge of the data collection and storage for an entire region. While much of the tradition is being lost, some indigenous villages use quipus to register crops and community animals[5].
According the Bernabé Cobo[6], a Jesuit Chronicler, the Incans further developed a specialist for accounting-related tasks. Known as quipo camayos, incans placed full trust in them. Another researcher[7] observed that upon closing accounting books, certain numbers had to be ordered according their values in the agricultural calendar. The khipukamayuq was directly responsible for the correct placement of these values.
References
edit- ^ Contenido aparejable con los diccionarios de 'matemática en quechua' en uso actual y los instrumentos conocidos: quipo y yupana
- ^ Ascher M. y Ascher R. (1985). Heather Lechtman, Ana María Soldi (ed.). La tecnología en el mundo andino. México D.F.: UNAM. ISBN 9789688372937.
- ^ Kubler, George (1947-08-01). "Los orígenes de los inkas". Hispanic American Historical Review. 27 (3): 561–562. doi:10.1215/00182168-27.3.561. ISSN 0018-2168.
- ^ Corral, Rose (2018-11-19). "«En el hoy de ayer, en el ayer de hoy»". América (52): 83–89. doi:10.4000/america.2399. ISSN 0982-9237.
- ^ Rostworowski de Diez Canseco, María (1953-06-23). "La sucesión monárquica y el co-reinado entre los incas". Letras (Lima). 19 (49): 213–216. doi:10.30920/letras.19.49.17. ISSN 2071-5072.
- ^ Morong R, Germán (2019). "Melancolía y flema: dos atributos del indio en las obras de Lope de Atienza (1575) y Bernabé Cobo (1653)". Romance Notes. 59 (1): 51–61. doi:10.1353/rmc.2019.0005. ISSN 2165-7599.
- ^ Vidal Alangui, Wilfredo (2020-12-31). "Beyond songs and dances: Ethnomathematics and the challenge of culture". Revista Latinoamericana de Etnomatemática Perspectivas Socioculturales de la Educación Matemática. 13 (3): 88–107. doi:10.22267/relatem.20133.63. ISSN 2011-5474.