29 March 1999 Vol. 4, No. 13
THE MATH FORUM INTERNET NEWS
Internet Mathematics Library | Taxicab Geometry |
Mathematical Connections
INTERNET MATHEMATICS LIBRARY - The Math Forum
http://mathforum.org/library/
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:
http://mathforum.org/library/help.html
Some popular new starting points:
Mathematics Topics, from Algebra and Arithmetic to Statistics
and Topology...
http://mathforum.org/library/browse/static/topic/
Resource Types
http://mathforum.org/library/browse/static/resource_type/
- Lesson Plans and Activities
http://mathforum.org/library/browse/static/resource_type/lesson_plans.html
- Problems and Puzzles
http://mathforum.org/library/browse/static/resource_type/problems_puzzles.html
Mathematics Education Topics, including Teaching Issues
and Strategies, Research and Reform, and more
http://mathforum.org/library/browse/static/ed_topic/
We are now cataloguing only mathematics and math education
sites. We invite you to suggest a link:
http://mathforum.org/library/add/
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.
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WHAT IS TAXICAB GEOMETRY?
- selected Internet resources -
Taxicab Geometry - Shunta, Graff, VanBelkum
http://www2.gvsu.edu/~vanbelkj/Project.html
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
http://math.rice.edu/~lanius/Geom/schbus1.html
A lesson that introduces a non-Euclidean geometry using a
school bus rather than a taxicab.
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Taxicab Geometry/La Géométrie des Taxis - Pascal Tesson
http://www-cgrl.cs.mcgill.ca/~godfried/teaching/projects.pr.98/tesson/taxi/644project.html
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.
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Taxicab Angles and Trigonometry - Thompson, Dray
http://home.rmi.net/~nivek/taxicab/
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.
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MATHEMATICAL CONNECTIONS - Whittle, Luoma
http://www.aug.edu/dvskel/
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.
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