Abstract
This paper is about the South American indigenous group commonly called the Incas and their mathematics. The first term we must clarify is ‘Inca’, by which we refer to a collection of many groups who had a common government, religion and language, but were of distinct cultural origins. When we speak of the ‘Inca Empire’, we refer to the territory controlled by the Inca from about 1400 to 1560 AD, though we will see that there were other groups before and during those years that had significant influence on the Incas and their mathematics. The first Incas started near Cuzco in present-day Peru and persistently moved on neighboring groups until they formed an enormous empire that included part or all of Peru, Ecuador, Bolivia, Chile, Argentina, and southern Colombia.
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Bibliography
Alcina Franch, José and Josefina Palop Martinez. Los Incas, el Reino del Sol. Madrid: Ediciones Anaya, 1988.
Ascher, Marcia. Ethnomathematics: A Multicultural View of Mathematical Ideas. Pacific Grove, California: Brooks/Cole, 1991.
Ascher, Marcia. ‘Mathematical ideas of the Incas.’ In Native American Mathematics, Michael P. Closs, ed. Austin: niversity of Texas Press, 1986, pp. 261–289.
Ascher, Marcia. ‘The logical-numerical system of Inca quipus.’ Annals of the History of Computing 5(3): 268–278, 1983.
Ascher, Marcia and Robert Ascher. Code of the Quipu: A Study in Media, Mathematics, and Culture. Ann Arbor: University of Michigan Press, 1981. (Reprinted as Mathematics of the Incas: Code of the Quipu, New York: Dover Publications, 1997.)
Ascher, Marcia and Robert Ascher. Code of the Quipu: Databook. Ann Arbor: University of Michigan Press, 1978 and Code of the Quipu: Databook II. Ithaca, Ascher and Ascher, 1988 (on microfiche at Cornell University Archives, Ithaca, New York).
Aveni, Anthony, ed. The Lines of the Nazca. Philadelphia: The American Philosophical Society, 1990.
Buechler, Hans and Judith-Maria Buechler. The Bolivian Aymara. New York: Holt, Rinehart and Winston, 1971.
Burns Glynn, William. Legado de los Amautas. Lima: Editora Ital Peru, 1990.
Burns Glynn, William. La Escritura de los Incas. Boletin de Lima, No. 12, 13, 14. Lima: Editora Los Pinos, 1981.
Closs, Michael P., ed. Native American Mathematics. Austin: niversity of Texas Press, 1986. D’Ambrosio, U. Etnomatematica. Sao Paulo: Editora Atica, 1990.
Gallian, Joseph. Contemporary Abstract Algebra. 4th ed. Boston: Houghton-Mifflin, 1998.
Guaman Poma de Ayala, Felipe. El Primer Nueva Corónica y Buen Gobierno (1614), Paris: Université de Paris Istitut d’Ethnologie, 23, 1936. (Original manuscript at Det Kongelige Bibliotek, Copenhagen, Denmark.)
Hadingham, Evan. Lines to the Mountain Gods; Nazca and the Mysteries of Peru. New York: Random House, 1987.
Higuera Acevedo, Clara L. ‘La yupana Incaica: Elemento histórico como instrumenta pedagógico.’ In Proceedings of the Meeting of the International Study Group on Relations between History and Pedagogy of Mathematics, Sergio Nobre, ed. Brazil: NESP, 1994, pp. 77–89.
Lara, Jesus. La Literatura de los Quechuas. Cochabamba, Bolivia: ditorial Canelas, 1960.
Mackey, Carol and Hugo Pereyra, Carlos Radicati, Humberto Rodriguez, Humberto and Oscar Valverde, eds. Quipu y Yupana, Colección de Escritos. Lima: CONCYTEC, 1990.
Mannheim, Bruce. The Language of the Inka Since the European Invasion. Austin: University of Texas Press, 1991.
Mannheim, Bruce. ‘Southern Peruvian Quechua.’ In South American Indian Languages, Retrospect and Prospect, Harriet E. Manelis and Louisa S. Stark, eds. Austin: University of Texas Press, 1985, pp. 481–515.
Moseley, Michael E. The Incas and Their Ancestors; The Archeology of Peru. London: Thames and Hudson, 1992.
Myers, Sarah. Language Shift Among Migrants to Lima, Peru. Chicago: University of Chicago Department of Geography, Research Paper no. 147, 1973.
Pacheco, Oscar. Ethnogeometria. Santa Cruz (Bolivia): Editorial CEPDI BOLIVIA, 1997.
Paternosto, César. The Stone and the Thread; Andean Roots of Abstract Art, trans. Esther Allen. Austin: University of Texas Press, 1996.
Radicati di Primeglio, Carlos. ‘Tableros de escaques en el antiguo Perú.’ In Quipu y Yupana, Colección de Escritos, Carol Mackey et al., eds. Lima: CONCYTEC, 1990, pp. 219–234.
Schneider, Mary Jane. North Dakota Indians, An Introduction. Dubuque, Iowa: Kendall/Hunt, 1994.
Stark, Louisa R. ‘Ecuadorian highland Quechua: history and current status.’ In South American Indian Languages, Retrospect and Prospect, Harriet E. Manelis and Louisa S. Stark, eds. Austin: niversity of Texas Press, 1985, pp. 443–479.
Stark, Louisa R. ‘The Quechua language in Bolivia.’ In South American Indian Languages, Retrospect and Prospect, Harriet E. Manelis and Louisa S. Stark, eds. Austin: University of Texas Press, 1985, pp. 516–545.
Urton, Gary. The Social Life of Numbers, A Quechua Ontology of Numbers and Philosophy of Arithmetic. Austin: University of Texas Press, 1997.
Wassén, Henry. ‘El antiguo abaco peruano según el manuscrito de Guaman Poma.’ In Quipu y Yupana, Colección de Escritos, Carol Mackey et al., eds. Lima: ONCYTEC, 1990, pp. 205–218.
Weber, John David. A Grammar of Huallaga (Huânuco) Quechua. Berkeley: University of California Press, 1989.
Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Culture. Chicago: Lawrence Hill Books, 1973.
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Gilsdorf, T.E. (2000). Inca Mathematics. In: Selin, H. (eds) Mathematics Across Cultures. Science Across Cultures: The History of Non-Western Science, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4301-1_11
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DOI: https://doi.org/10.1007/978-94-011-4301-1_11
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