*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

*Circles in
Taxicab Geometry*

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

This affects what the circle looks like
in each geometry.

In both geometries
the circle is defined the same:

the set of all
points that are equidistant from a single point.

The set of all
points that are the same Euclidean distance from a single point look like:

*Here the circle
is defined as the set of all *

*points that are
a distance of 3 from A.*

The set of all
points that are the same taxicab distance from a single point look like:

*This circle is
also defined as the set of all *

*points that are
a distance of 3 from A.*