Foundations of Geometry I Project
University of Georgia
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.
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.