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Whitney umbrella

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In geometry, the Whitney umbrella or Whitney's umbrella, named after American mathematician Hassler Whitney, and sometimes called a Cayley umbrella, is a specific self-intersecting ruled 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 which is parallel to the axis of the parabola and lies on its perpendicular bisecting plane.