*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

*Perpendicular
Bisectors in Taxicab Geometry*

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

This affects what the perpedicular
bisector looks like in each geometry.

In both geometries
the perpendicular bisector of a line segment is defined the same:

The set of all
points that are equidistant from the endpoints of the line segment.

In the Euclidean
plane the perpendicular bisector looks like:

*Here the
perpendicular bisector of segment AB*

*is defined as
the set of all points where the AC = BC.*

*GeometerŐs Sketchpad Animation *

In the taxicab
plane the perpendicular bisector looks like:

*Here the
perpendicular bisector is defined as the set of all points *

*where taxicab
distance AC = taxicab distance CB*

*GeometerŐs Sketchpad Animation *