TAXICAB GEOMETRY
by
Susan Sexton
Foundations of
Geometry I Project
University of
Georgia
Fall 2006
Instructor: Clint
McCrory
Hyperbolas in
Taxicab Geometry
The notion of
distance is different in Euclidean and taxicab geometry.
This affects what the hyperbola looks
like in each geometry.
In both geometries
the hyperbola is defined the same:
The set of all
points where the difference of the distances from
two fixed points to
a point in the set is constant.
In the Euclidean
plane the hyperbola looks like:
Here the
hyperbola is defined as the set of all points where the AB - AC = 3
GeometerŐs
Sketchpad Animation
In the taxicab
plane the hyperbola looks like:
Here the
hyperbola is defined as the set of all points
where taxicab
distance AC - taxicab distance CB = 3
