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Topic: Taxicab Geometry
Replies: 3   Last Post: Feb 24, 1995 3:10 PM

 Messages: [ Previous | Next ]
 F. Alexander Norman Posts: 141 Registered: 12/3/04
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 Non-Euclidean 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) 455-6136 (Work)
> \__________| (206) 746-5449 (FAX)
> (206) 883-6087 (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 non-collinear 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

Date Subject Author
2/22/95 Art Mabbott
2/22/95 Doris Schattschneider
2/24/95 F. Alexander Norman
2/24/95 Henri Picciotto