Whitney umbrella
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Section of the surface
In mathematics, specifically in the field of singularity theory, the Whitney umbrella (also referred to as Whitney's umbrella) is a self-intersecting rectangle placed in three dimensions.
It can be given by the parametric equations
(which is just the rectangle in 3-space.)
or by the implicit equation
- x2z − y2 = 0
which also include the negative z axis (which is called the handle of the umbrella).
It is a local model of a pinch point singularity, which is the only stable singularity of maps 
.
It is named after the American mathematician Hassler Whitney.
[edit] See also
[edit] References
- Whitney's Umbrella. The Topological Zoo. The Geometry Center. Retrieved on 2006-03-08. (Images and movies of the Whitney umbrella.)
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