To expand search, see The Reckoning of Time. Laterally related topics: The Sundial and The Clock.
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, Astronomy, Angular Measure, Agriculture, The Kenyah, The Kayan, Java, The Dyak, The Maloh, and The Iban.
Angell, Ian O. Megalithic mathematics, ancient almanacs or neolithic nonsense. Bull. Inst. Math. Appl. 14 (1978), no. 10, 253--258. (Reviewer: C. R. Fletcher.) SC: 01A10, MR: 80f:01002.
Discusses different explanations for the shapes of megalithic stone rings. The author briefly discusses some of the theories of Alexander Thom, which involve an astronomical calendar and an effort to make the circumference equal to 3 times the "diameter" rather than the irrational pi. He then discusses two new theories of his own. One explains the shapes of the stone rings as extensions of the ellipse, generated with three or four pegs and a string rather than with just the usual two. The other explains the shapes as an effort to store shadow lengths. Neither theory may be given entirely in earnest. A theme of the paper is how theories may start as intellectual games, go out of control, and be changed into pseudo-science. Closely related topics: The Stone Builders, Astronomy, The Ellipse, Pseudoscience, and Alexander Thom.
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 Quipu, The Maya, Astronomy, and Chinese Remainder Problems.
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: Ancient Egypt, Sumerians and Babylonians, The Roman Empire, Greece, The Islamic World, India, China, Japan, Vietnam, Java, Bali, The Maya, Guatemala (and Cakchiquel Indians), France in the 1700s, The Jewish Tradition, and Religion.