*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

*Ellipses in
Taxicab Geometry*

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

This affects what the ellipse looks like
in each geometry.

In both geometries
the ellipse is defined the same:

The set of all
points where the sum of the distances from two fixed points to a point in the
set is constant.

In the Euclidean
plane the ellipse looks like:

*Here the ellipse
is defined as the set of all points where the AC + CB = 6*

*GeometerŐs
Sketchpad Animation
*

In the taxicab
plane the ellipse looks like:

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

*where taxicab
distance AC + taxicab distance CB = 9*

*GeometerŐs Sketchpad
Animation
*