Whitney Umbrella

A surface with a pinch-point singularity

← Back to Index

About

The Whitney umbrella is a surface in three dimensions that exhibits a pinch-point singularity. It is one of the simplest and most iconic examples of a singular surface, demonstrating how smooth geometry can break down at certain points.

This surface is defined parametrically as: (u,v) → (u v, u, v²), showing its characteristic self intersection along a half-line, and pinch at the origin.

Interactive Model