To refine search, see subtopic Leveling. To expand search, see Time and Space. Laterally related topics: The Reckoning of Time, Astronomy, Geodesy, Cartography, and Navigation.
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.
Deshpande, M. N. Archaeological sources for the reconstruction of the history of sciences of India. Indian J. History Sci. 6 (1971), 1--22. (Reviewer: A. I. Volodarskii.) SC: 01A25 (01A10), MR: 58 #15813.
A broad review of the archaeology of ancient India, focusing on the sciences. Perhaps a third of the article is devoted to a discussion of the Harappan civilization, and particularly Harappa and Mohenjo-Daro. Little is directly known about Harappan mathematics, but there are strong suggestions that there would have been some significant knowledge of surveying and possibly astronomy. The author also discusses the Harappan system of weights and measures. A good area for future research, particularly if some progress is made in reading the Harappan script. Closely related topics: The Harappan Civilization, Astronomy, The Balance and the Measurement of Weight, The Measurement of Distance, and Archaeology.Modify notes on this entry Modify bibliography entry Make comment on this entry
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, Cartography, Banking, Taxation, The Reckoning of Time, Games, Numerology, and Number Systems.Modify notes on this entry Modify bibliography entry Make comment on this entry
Eves, Howard. On the Practicality of the Rule of False Position. Mathematics Teacher 51 (1958), 606--8.
Eves shows how the method of false position can be simpler than our own methods by giving one example from the Ahmes Papyrus, three from the Greek Anthology of c. 500 AD, and two of his own. One of his examples is from surveying, and Eves says that it is the method a surveyor would probably use. In the other example of his own, he likens the rule of false position to the method of similitude in geometric constructions. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: The Method of False Position, Ancient Egypt, Medieval Europe, and Geometry.Modify notes on this entry Modify bibliography entry Make comment on this entry
Fields, Margaret. Practical Mathematics of Roman Times. Mathematics Teacher 26 (1933), 77--84.
Surveys Roman mathematics. Some of the most interesting examples come from the De Architectura of Vitruvius, which discusses principles of symmetry and proportion and how to use them in architecture. Vitruvius goes as far as how to correct for an optical illusion on the capitals of columns. He also discusses geometric procedures to be used in laying out a town (to shut out winds), and various Roman instruments, including leveling instruments and an instrument for measuring distance called a hodometer. The hodometer is used for "telling the number of miles while sitting on a carriage or sailing by sea", and is particularly ingenious. Second to Vitruvius, the most important source on Roman engineering may be the Urbis Romae of Frotinus, which includes mathematical rules (not entirely successful) to determine the flow of an aqueduct. Surviving Roman bridges show a high level of skill; there were surely mathematical principles behind their design, but no detailed study has survived. Roman tunnels are equally impressive. Heron discusses how to use an instrument called the "dioptra" to survey for tunnels, measure the width of a river, and so on. Roman sundials were relatively unsophisticated. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Vitruvius, Architecture, Symmetry, Proportion and the Golden Ratio, Optics, Leveling, The Measurement of Distance, Frotinus, Heron, and The Sundial.Modify notes on this entry Modify bibliography entry Make comment on this entry
Fischer, Irene K. At the dawn of geodesy. Bull. Géodésique 55 (1981), no. 2, 132--142. SC: 01A10 (01A17 01A20 01A25), MR: 83g:01002.
The cultures in ancient Egypt and in Greece, China, and Babylonia all did work in surveying, geodesy, and astronomy. However, they all had different approaches to the subjects. The author explains that "The striking difference between the abstract, geometric approach of Greece and the concrete, algebraic approach of Babylonia and China represent not a difference in talents but a difference in culture-bound interests." The reader should probably have some prior knowledge of the subject matter (and of geodesy in particular) to fully appreciate this article. Closely related topics: Astronomy, Ancient Egypt, Greece, China, and Sumerians and Babylonians.Modify notes on this entry Modify bibliography entry Make comment on this entry
Høyrup, Jens. Sub-scientific mathematics: observations on a pre-modern phenomenon. Hist. of Sci. 28 (1990), no. 79, part 1, 63--87. (Reviewer: David Singmaster.) SC: 01A10 (01A05 01A12 01A80), MR: 91j:01007.
Høyrup makes a distinction between scientific and subscientific mathematics. These fields correspond somewhat to pure and applied mathematics. However, by using this new terminology, the author hopes to avoid suggesting that "subscientific" mathematics is always derived from "scientific" mathematics in the way that "applied" mathematics is derived from "pure" mathematics. Høyrup discusses the distinction between scientific and subscientific mathematics and also their various kinds of relationships. His examples are drawn from Greece, Egypt, India, the Islamic World (with references to the Silk route), and from the Carolingian Propositiones ad acuendos jevenes. (The latter is traditionally associated with Alcuin.) Høyrup touches on relevant work by the mathematicians Hero, Diophantus, and al Khwarizmi. Surveying is discussed as a particularly important type of subscientific mathematics. Closely related topics: Applied Mathematics (General), Greece, Ancient Egypt, India, The Islamic World, Alcuin, Heron, Diophantus, and Abu Abdullah Muhammed ibn Musa al Khwarizmi.Modify notes on this entry Modify bibliography entry Make comment on this entry
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