Superellipses and Superhyperbolas: Beyond Classical Geometry

2025-03-28

This article introduces superellipses and superhyperbolas, generalizations of ellipses and hyperbolas, respectively. The shapes are controlled by a parameter 'p'. When p=2, they reduce to standard ellipses and hyperbolas. Increasing p makes superellipses more rectangular, but with continuous curvature; superhyperbolas become blunted at the vertices. The article explores why superellipses are far more common than superhyperbolas, speculating on naming conventions and the lack of effective advocacy for the latter.