page_title: Whitney umbrella
section_title: Properties
hierarchical_section_title: Whitney umbrella / Properties
caption_attribution_description: English: Whitney umbrella made of a single string on a plastic box
context_page_description: In mathematics, the Whitney umbrella is a specific self-intersecting surface placed in three dimensions. It is the union of all straight lines that pass through points of a fixed parabola and are perpendicular to a fixed straight line, parallel to the axis of the parabola and lying on its perpendicular bisecting plane.
context_section_description: Whitney's umbrella is a ruled surface and a right conoid. It is important in the field of singularity theory, as a simple local model of a pinch point singularity. The pinch point and the fold singularity are the only stable local singularities of maps from R² to R³.
  It is named after the American mathematician Hassler Whitney.
  In string theory, a Whitney brane is a D7-brane wrapping a variety whose singularities are locally modeled by the Whitney umbrella. Whitney branes appear naturally when taking Sen's weak coupling limit of F-theory.
caption: Whitney umbrella made with a single string inside a plastic cube
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