Pinch point (mathematics)

In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface. The equation for the surface near a pinch point may be put in the form where [4] denotes terms of degree 4 or more and is not a square in the ring of functions. For example the surface near the point , meaning in coordinates vanishing at that point, has the form above. In fact, if and then {} is a system of coordinates vanishing at then is written in the canonical form. The simplest example of a pinch point is the hypersurface defined by the equation called Whitney umbrella.

Pinch point (mathematics)

In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface. The equation for the surface near a pinch point may be put in the form where [4] denotes terms of degree 4 or more and is not a square in the ring of functions. For example the surface near the point , meaning in coordinates vanishing at that point, has the form above. In fact, if and then {} is a system of coordinates vanishing at then is written in the canonical form. The simplest example of a pinch point is the hypersurface defined by the equation called Whitney umbrella.