TAXICAB GEOMETRY
by
Susan Sexton
Foundations of
Geometry I Project
University of
Georgia
Fall 2006
Instructor: Clint
McCrory
Ellipses in
Taxicab Geometry
The notion of
distance is different in Euclidean and taxicab geometry.
This affects what the ellipse looks like
in each geometry.
In both geometries
the ellipse is defined the same:
The set of all
points where the sum of the distances from two fixed points to a point in the
set is constant.
In the Euclidean
plane the ellipse looks like:
Here the ellipse
is defined as the set of all points where the AC + CB = 6
GeometerŐs
Sketchpad Animation
In the taxicab
plane the ellipse looks like:
Here the ellipse
is defined as the set of all points
where taxicab
distance AC + taxicab distance CB = 9
GeometerŐs Sketchpad
Animation
