To expand search, see Indo-Malay Archipelago. Laterally related topics: The Kenyah, The Kayan, The Dyak, The Maloh, The Iban, The Belu of Central Timor, and Bali.
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.
Ammarell, Gene. Sky calendars of the Indo-Malay archipelago. History of oriental astronomy (New Delhi, 1985), 241--247, Cambridge Univ. Press, Cambridge, 1987. SC: 01A13 (01A07), MR: 1 160 818.
The people of the Indo-Malay archipelago used astronomical events such as the heliacal risings or culminations of stars, the solstices, and the zenith sun to make calendars or otherwise determine the most favorable time for rice planting. There is sometimes a need to measure or mark angles in this context, and methods used include shadow methods (marking the lengths of the tangents on some sticks), an ingenious method of tilting a bamboo stick filled with water, and a method of noting when kernels of rice rolled off an open palm when raised to Orion at dusk. (In the case of one tribe, someone observed that "the time was right for planting when a man looked up to see the Pleiades and his fat fell off!") Closely related topics: Indo-Malay Archipelago, The Calendar, Astronomy, Angular Measure, Agriculture, The Kenyah, The Kayan, The Dyak, The Maloh, and The Iban.
Aveni, A. F. Tropical archeoastronomy. Science 213 (1981), no. 4504, 161--171. (Reviewer: M. P. Closs.) SC: 01A10, MR: 82j:01006.
Cultures in the tropics appear in general to have adopted a horizon and zenith approach to the sky, as opposed to the approach with the celestial pole (now Polaris) and the ecliptic/celestial equator, which is more familiar to most of us. Arorae in the Gilbert Islands (Kiribati) is very close to the equator, and navigators used stars on the horizon instead of compass directions. To them, constellations were also long chains of stars. Apparently, the people of the Caroline Islands also used a kind of star compass. In Polynesia and apparently in much of Oceania, islands were associated with stars that have zenith appearances above them; this is also useful in navigation. The Maori used a similar system. Various cultures in central and south America have been particularly interested in horizon and zenith events. These include the Maya, the Inca, and the Aztec, and are discussed in detail. There was a similar interest in the Chalchihuites culture, apparently influenced by astronomers of the Teotihuacán empire. Less is known about astronomy in Africa, but the Mursi of Ethiopia appear to corroborate the author's thesis, as may the Bambara of Sudan as well. Closely related topics: Astronomy, Kiribati (The Gilbert Islands), The Hawaiians, The Caroline Islands, Navigation, The Maya, The Chalchihuites, The Teotihuacán Empire, The Inca, The Aztec, Oceania, The Mursi of Ethiopia, The Bambara of Sudan, and The Maori.
Kudlek, Manfred. Calendar systems. Mathematische Wissenschaften gestern und heute. 300 Jahre Mathematische Gesellschaft in Hamburg, Teil 2. Mitt. Math. Ges. Hamburg 12 (1991), no. 2, 395--428. (Reviewer: J. S. Joel.) SC: 01A99 (00A69), MR: 92j:01079.
A rare and unusually wide ranging look at calendar systems in a variety of cultures. Explains some of the astronomical issues involved. The author discusses calendars of Egypt, Babylonia, the Roman Empire, Greece (Athens), the Islamic World (especially Persia), India, China (only gives a taste, since more than 50 official calendars were used), Japan and Vietnam (their calendars were connected with China), Java, Bali, Guatamala (by the Cakchiquel Indians), revolutionary France, the Mayas, and in the Jewish tradition. Discusses the computation of the date of Easter. (The computation of Easter was of course one of the primary goals of mathematics instruction in the middle ages.) There is information on how to correlate these calendars as well (in terms of Julian dates). Closely related topics: The Calendar, Ancient Egypt, Sumerians and Babylonians, The Roman Empire, Greece, The Islamic World, India, China, Japan, Vietnam, Bali, The Maya, Guatemala (and Cakchiquel Indians), France in the 1700s, The Jewish Tradition, and Religion.