To expand search, see Time and Space. Laterally related topics: The Reckoning of Time, Astronomy, Geodesy, Cartography, and Surveying.
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. Models and maps from the Marshall Islands: a case in ethnomathematics. Historia Math. 22 (1995), no. 4, 347--370. SC: 01A07 (01A13), MR: 1 364 080.
The Marshall islanders used their understanding of swell interaction to navigate, rather than the astronomical methods more familiar to us. These methods had the advantage of being usable when the sky was not visible. In fact, the author notes "one navigator recounted that an early part of his training was begin made to float in water at various places in order to learn how to feel what would later be shown and explained to him." Ascher explains how wave refraction and reflection explain the swell interactions, and how the Marshall islands map called the mattang was used to explain these interaction. She explains how the rebbelith and meddo maps (large and smaller scale) are not just literal descriptions of distances, but are also abstract representations of some of the same principles. Closely related topics: The Marshall Islands and Cartography.Modify notes on this entry Modify bibliography entry Make comment on this entry
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, The Maya, The Chalchihuites, The Teotihuacán Empire, The Inca, Java, The Aztec, Oceania, The Mursi of Ethiopia, The Bambara of Sudan, and The Maori.Modify notes on this entry Modify bibliography entry Make comment on this entry
Court, Nathan Altshiller. Mathematics in the History of Civilization. The Mathematics Teacher 41 (1948), 104--11.
How different concerns of society influenced mathematics. How the development of the concept of number is reflected in language. How the concept of how many led to arithmetic. How the concept of how much led to geometry. (Taxation and agriculture also contributed to both.) Efforts to keep time led to trigonometry. Navigation and associated astronomical problems led to logarithms [and more trigonometry]. Problems in artillery led to graphs. Both required an understanding of motion. Analytic geometry and calculus were invented in part to better understand motion. Statistics developed to understand problems in the social sciences. Also discusses the nature of mathematics: mathematics for its own sake and the axiomatic method. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Why Study History Of Math, Mathematics in Language, Number Systems, Arithmetic, Geometry, Taxation, Agriculture, Astronomy, The Reckoning of Time, Trigonometry, Artillery, Graphing, Dynamics, Force, and Motion, Analytic Geometry, Calculus, Statistics, Social Science, and Proof.Modify notes on this entry Modify bibliography entry Make comment on this entry
Proverbio, Edoardo. The contribution of the mechanical clock to the improvement of navigation. Longitude zero 1884--1984 (Greenwich, 1984). Vistas Astronom. 28 (1985), no. 1-2, 95--103. SC: 01A99, MR: 809 625.
It is a relatively simple matter to measure latitude with simple instruments; your latitude is for example nearly equal to the altitude of the pole star above your horizon. Longitude can in theory be determined by what amounts to determining your time zone; this can be determined by noting the time of sunrise. If you note that the sun rises three hours later than it did at home, you would expect to be about 3 time zones, or 45 degrees to the west of home. However, until the mid 1700s, there was no accurate way to keep track of time at sea; traditional methods such as water clocks were hopeless on a moving ship. A solution was proposed by the mathematician and astronomer Galileo, who discovered the moons of Jupiter. These moons occasionally eclipse each other, and if one could predict when that would happen, one would in effect have a clock in the sky. Other mathematical/astronomical methods were proposed as well; in theory if you have accurate enough predictions of the orbit of the moon, you can predict time by observations of the moon as well. Unfortunately, mathematical methods were not yet adequate to predict the positions of astronomical objects with enough accuracy, and the computations could have been difficult for the average sailor in any case. So attention began to focus again on finding a more accurate clock. Some of the problems in clock design involved mathematics as well. For example, it was known that a pendulum will swing in roughly equal time regardless of the size of the swing. (A famous story tells of how Galileo discovered this in church one day, by comparing with his pulse.) "Roughly equal" wasn't good enough, and a mathematically very interesting solution was suggested by the mathematician and scientist Christiaan Huygens. His suggestion involved improving the accuracy of the pendulum by using the tautochrone property of the cycloid. Huygens tried a number of other things as well. Of course, there is much more that doesn't involve mathematics so directly. A fascinating article. Closely related topics: The Reckoning of Time, The Clock, Astronomy, Galileo Galilei, Christiaan Huygens, and The Cycloid.Modify notes on this entry Modify bibliography entry Make comment on this entry
Modify this category Add bibliography entry Make comment on this category