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.

Geometer’s 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

Geometer’s Sketchpad Animation

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