Whitney umbrella

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.

Whitney's umbrella can be given by the parametric equations in Cartesian coordinates where the parameters u and v range over the real numbers.

It is also given by the implicit equation This formula also includes the negative z axis (which is called the handle of the umbrella).

Whitney's umbrella is a ruled surface and a right conoid.

Whitney branes appear naturally when taking Sen's weak coupling limit of F-theory.