Surfaces49 of 113
Whitney umbrella
Hassler Whitney, 1943
The simplest way a smooth map can fail to be smooth: a surface that crosses itself along a line, and that line stops at a pinch point, the tip of the handle. Whitney showed every generic map from a surface into space has only crossings, triple points and these pinches.
(uv, u, v²)
On mathcurve.com as Parapluie de Whitney
Drawn as