*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

*Parabolas in
Taxicab Geometry*

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

This affects what the parabola looks
like in each geometry.

In both geometries
the parabola is defined the same:

The set of all
points that are equidistant from a fixed point and a fixed line.

In the Euclidean
plane the parabola looks like:

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

*where AC is the
same distance as A to the line*

*and BC is the
same distance as B to the line.*

*GeometerŐs
Sketchpad Animation
*

In the taxicab
plane the parabola looks like:

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

*where taxicab
distance AC = taxicab distance of A to the line*

*and taxicab
distance CB = taxicab distance of B to the line.*

*GeometerŐs
Sketchpad Animation
*