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Re: Taxicab Geometry
Posted:
Feb 24, 1995 4:30 AM


On Wed, 22 Feb 1995, Art Mabbott wrote:
> I hope that someone out there can provide me with some help. I am > working my way through the small paperback book "Taxicab Geometry  An > Adventure in NonEuclidean Geometry" by Eugene F. Krause with a topics > class .... <stuff deleted> > > Art Mabbott > ****************************************************************************** > mabbotta@belnet.bellevue.k12.wa.us > __ _______ >   /  Newport High School >  `'*  4333 128th Ave. S.E. >   Bellevue, WA 98006 > _  (206) 4556136 (Work) > \__________ (206) 7465449 (FAX) > (206) 8836087 (Home) >
I am currently using this book in both a graduate geometry course and an undergraduate course for elementary math specialists and secondary mathematics teachers. There are any number of interesting questions that could serve as a core for an investigative paper. We have been keen on analysing the differences and similarities between Euclidean and taxicab geometries that aren't explicit in the book.
For example, your students might investigate questions like the following:
How might we calculate area in TG?
Find a "nice" expression for the area of an ellipse? (Is there a analogous expression to the Euclidean \pi*a*b?
In EG three noncollinear points determine a unique circle? In TG? Can you find simple conditions for points to determine a TG circle?
What is the TG analog of median of a triangle? Centroid? Altitude?
What is the proper notion of symmetry in TG?
What does it mean for two triangles (or other figures) to similar? congruent?
Generalize TG to three dimensions?
. . .
By the way, I have used Sketchpad to demonstrate many of the problems in TG  pretty effectively I think.
Cheers!
Sandy Norman UT San Antonio



