To refine search, see subtopic Joseph Louis Lagrange. To expand search, see France and The 1700s. Laterally related topics: France in the 1600s, France in the Middle Ages, Switzerland in the 1700s, Russia in the 1700s, Austria in the 1700s, Germany in the 1700s, and The United States in the 1700s.
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.
Cox, Steven J. The shape of the ideal column. Math. Intelligencer 14 (1992), no. 1, 16--24. (Reviewer: Peeter Müürsepp.) SC: 01A99 (00A69), MR: 93a:01072.
Discusses the shape of the "ideal" column. Shows how the aesthetic and perceptual ideals of Greek and Roman times were relayed by Vitruvius and later by Alberti and others. Then shows how later scientists considered the problem from the point of view of structural strength instead. A key player in this new point of view was Lagrange. The author discusses mistakes in Lagrange's work and in the work of some later scientists and mathematicians. It is interesting that the author himself has made investigations in this area (together with M. L. Overton). The article Kirmser, Philip G. and Hu, Kuo-Kuang, The shape of the ideal column reconsidered is critical of these investigations, and includes a response by Cox. Closely related topics: The Column, Vitruvius, Leone Battista Alberti (1404?--1472), Statics, and Joseph Louis Lagrange.
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: Cartography and Graph Theory.
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, Java, Bali, The Maya, Guatemala (and Cakchiquel Indians), The Jewish Tradition, and Religion.