Foundations of Geometry I Project
University of Georgia
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.
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