To expand search, see The Inca and Number Systems. Laterally related topics: The Hindu-Arabic Numerals, TallySystems, and Finger Numerals.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Ascher, Marcia. Before the conquest. Math. Mag. 65 (1992), no. 4, 211--218. SC: 01A12, MR: 93g:01006.
Discusses the Inca and the Maya. With the Inca, focuses on the quipu. Most quipus were destroyed by the Spanish, who thought them to be the work of the Devil, but some 550 remain. Discusses their basic structure. A fascinating puzzle in the article is a pair of quipus which seem to represent data in a similar yet inexplicable way. With the Maya, focuses on their calendar. Again, much has been destroyed. For example, there only four codices remain, whereas thousands were burned by the Spanish. Fortunately, many stelae still exist. These show a calendar system with a variety of cycles. These cycles to us suggest Chinese Remainder problems. Examples of cycles are the 260 day ritual almanac composed of a cycle of 13 numbers and 20 named dieties, the vague year of 365 days composed of a cycle of 20 numbers within a cycle of 18 named dieties plus 5 unnamed days, their least common multiple (the calendar round of 18,980 days), the long count of days (in effect, multiples of 360 days plus a remainder), a 9 day cycle of Lords of the night associated with gods of the underworld, a lunar cycle of 29 and 30 day months, 13 levels in the heaven, a cycle of 4 cardinal directions (associated with different colors), sometimes used in conjunction with an 819 day cycle of the rain god. The Mayans appear to have had keen astronomical knowledge. The author notes that the error between real and tabulated times of the position of Venus would be off by just two hours in 500 years. Closely related topics: The Inca, The Maya, The Calendar, Astronomy, and Chinese Remainder Problems.Modify notes on this entry Modify bibliography entry Make comment on this entry
Ascher, Marcia. The logical-numerical system of Inca quipus. Ann. Hist. Comput. 5 (1983), no. 3, 268--278. (Reviewer: M. P. Closs.) SC: 01A12 (68-03), MR: 85b:01003.
Spanish chroniclers have claimed that the messages on quipus "were as varied as ballads, peace negotiations, laws, and state history." The approximately 550 quipus that still exist show us instead a variety of remarkable ways for organizing structured data. The meaning of this data, however, has been largely lost. Numbers in some quipus show relationships that are still hard to explain.Modify notes on this entry Modify bibliography entry Make comment on this entry
Diana, Lind Mae. The Peruvian Quipu. Mathematics Teacher 60 (1967), 623--28.
An introduction to the Quipu. The author observes that the quipu was used not only in Peru but also in other areas of South America. These others have not been as well preserved as those found in dry graves in coastal Peru. Discusses Nordenskiöld's theory that the burial quipus contain numerological and astronomical secrets. Briefly discusses the unusual Incan abacus. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: The Maya, Numerology, Astronomy, and The Abacus.Modify notes on this entry Modify bibliography entry Make comment on this entry
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