Foundations of Geometry I Project
University of Georgia
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
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