Math Forum Internet News

Volume 4, Number 13

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29 March 1999                                  Vol. 4, No. 13


Internet Mathematics Library | Taxicab Geometry |
Mathematical Connections INTERNET MATHEMATICS LIBRARY - The Math Forum The Forum's Internet Resource Collection has become the new Internet Mathematics Library, offering many more categories, selected starting points, updated entries, and powerful browse and search functions. Read about the Math Library at: Some popular new starting points: Mathematics Topics, from Algebra and Arithmetic to Statistics and Topology... Resource Types - Lesson Plans and Activities - Problems and Puzzles Mathematics Education Topics, including Teaching Issues and Strategies, Research and Reform, and more We are now cataloguing only mathematics and math education sites. We invite you to suggest a link: You will find a link to the Math Library at the bottom of each of our pages. We hope you will find this enhanced presentation helpful as you look for mathematics sites on the Internet. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- WHAT IS TAXICAB GEOMETRY? - selected Internet resources - Taxicab Geometry - Shunta, Graff, VanBelkum Taxicab geometry, a metric system in which the points in space correspond to the intersections of streets in an ideal city where all streets run horizontally and vertically, provides an introduction to non-Euclidean geometry. It is very close to Euclidean geometry in its axiomatic structure, differing in only one theorem, side-angle-side; and it has a wide range of applications to problems in urban geography: while Euclidean geometry appears to be a good model of the "natural" world, taxicab geometry is a better model of the artificial urban world that man has built. School Bus Geometry - Lanius A lesson that introduces a non-Euclidean geometry using a school bus rather than a taxicab. \|/ Taxicab Geometry/La Géométrie des Taxis - Pascal Tesson A term project in English and French for a Pattern Recognition course given by Godfried Toussaint at McGill University. Contents: - What is taxicab geometry? - Why taxicab geometry? - Voronoi Diagrams in taxicab geometry: a java applet - Related links and bibliography. \|/ Taxicab Angles and Trigonometry - Thompson, Dray Taxicab geometry is essentially the study of an ideal city with all roads running horizontal or vertical. The roads must be used to get from point A to point B; thus, the normal Euclidean distance function in the plane needs to be modified. A natural analogue to angles and trigonometry is developed; this structure is then analyzed to see which, if any, similar triangle relations hold, and an application involving the use of parallax to determine the exact (taxicab) distance to an object is discussed. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- MATHEMATICAL CONNECTIONS - Whittle, Luoma A forum for exploring the interplay between mathematics and the humanities, including, but not limited to, the relation between mathematics and the arts, anthropology, history, literature, philosophy, music, and religion. Classroom applications of these topics, such as the use of history in the teaching of mathematics, also fall within the scope of this periodical. The current issue and an archive of past issues (dating back to fall 1998) are available, as well as author guidelines. Mathematical Connections is indexed by the ERIC Clearinghouse for Science, Mathematics, and Environmental Education. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum Ask Dr. Math Problems of the Week Mathematics Library Teacher2Teacher Discussion Groups Join the Math Forum Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \

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