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
