*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

*Hyperbolas in
Taxicab Geometry*

The notion of
distance is different in Euclidean and taxicab geometry.

This affects what the hyperbola looks
like in each geometry.

In both geometries
the hyperbola is defined the same:

The set of all
points where the difference of the distances from

two fixed points to
a point in the set is constant.

In the Euclidean
plane the hyperbola looks like:

*Here the
hyperbola is defined as the set of all points where the AB - AC = 3*

*GeometerŐs
Sketchpad Animation
*

In the taxicab
plane the hyperbola looks like:

*Here the
hyperbola is defined as the set of all points *

*where taxicab
distance AC - taxicab distance CB = 3*

*
GeometerŐs
Sketchpad Animation
*