Foundations of Geometry I Project
University of Georgia
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
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