To expand search, see Time and Space. Laterally related topics: The Reckoning of Time, Astronomy, Navigation, 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 Navigation.
Dilke, O. A. W. Mathematics and measurement. Reading the Past, 2. University of California Press, Berkeley, CA; British Museum Publications, Ltd., London, 1987. 64 pp. ISBN: 0-520-06072-5. (Reviewer: Richard L. Francis.) SC: 01A05 (01A15 01A20), MR: 89f:01003.
This very interesting book discusses many aspects of mathematics in the Roman empire, Egypt, Babylonia, Greece, and sometimes other cultures. The book discusses systems of measurement of length, area, volume, and weight, mathematical or para-mathematical subjects such as surveying, cartography, interest rates, taxes, time keeping, games, and numerology. Also discusses number systems. Much of the discussion on number systems may be familiar, but here there is also a little that may be a little less familiar, such as the use of Etruscan letters in the early Roman numerals. In a work of this scope, the author of the book is not to be faulted that there may be some disagreement with occasional facts. The discussions on the mathematics of the Romans are particularly interesting; there are few other studies touching on Roman mathematical practices at all. Closely related topics: The Roman Empire, Ancient Egypt, Sumerians and Babylonians, Greece, The Measurement of Distance, The Measurement of Area and Volume, The Balance and the Measurement of Weight, Surveying, Banking, Taxation, The Reckoning of Time, Games, Numerology, and Number Systems.
Hunt, J. N. House numbering in revolutionary Paris. Bull. Inst. Math. Appl. 31 (1995), no. 9-10, 145--145. SC: 01A99 (01A50), MR: 1 352 301.
A variety of systems for numbering houses were used in Paris, both before and after the Revolution. The author discusses several of these systems, each of which had at least one fatal flaw. For example, in one system, the same number could be used several times on one street, so that if you were dropped in the middle of a street and wanted to find a given address, it could be impossible to know what direction to proceed. After many unsuccessful attempts to develop a workable system, an "ordinary citizen by the name of Garros [proposed] the eminently reasonable system in which numbers were to be attached to successive doorways, odd numbers on the left and even numbers on the right, beginning from the end nearest to the centre of Pairs. Although Initially rejected for flimsy reasons such as 'It needed equal numbers of houses on each side,' or 'What about the banks of the Seine?,' it was generally well received." An earlier suggestion had also been kept, "to number houses in the direction of river flow for streets that were more or less parallel to the Seine, and away from the river for the remainder." As the author observes discussing one of the systems, "a Graph Theorist might devise a more convenient system", and indeed some of the issues involved could lead to interesting problems in graph theory. Closely related topics: France in the 1700s and Graph Theory.
Swetz, Frank J. Seeking Relevance? Try the History of Mathematics. Mathematics Teacher 77 (1984), 54--62.
Focuses on how the history of mathematics can be used to improve mathematics education. It can not only breath new life into the subject, but also allow students to better understand mathematics as a mode of inquiry. If students see mathematical ideas in other times [and in other cultures], they can appreciate the ideas better in our own. Swetz gives examples from the development of algorithms for arithmetic (including square roots). Ancient demonstrations of mathematical ideas, such as the "husan-thu" proof of the Pythagorean theorem from China can be conceptually more suitable for students than more synthetic modern ones. Ancient "homework problems" from Babylonia, China, and Medieval Italy can be more interesting than the more dry and formulaic modern equivalents. (See Swetz, Was Pythagoras Chinese? for many interesting examples from China.) Although the author doesn't discuss this, the Chinese problems in surveying led to interesting questions in algebra, with fourth and higher degree equations. Swetz discusses how Descartes' idea of a coordinate grid was earlier used by Renaissance artists, ancient Egyptian tomb painters, and various cartographers. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Education, Arithmetic, Computation, China, Algebra, Analytic Geometry, Renaissance Art, and Ancient Egypt.