High Quality Content by WIKIPEDIA articles! 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 f(u,v,w) = u^2 - vw^2 + [4] , where denotes terms of degree 4 or more and v is not a square in the ring of functions. For example the surface 1 ? 2x + x2 ? yz2 = 0 near the point (1,0,0), meaning in coordinates vanishing at that point, has the form above. In fact, if u = 1 ? x,v = y and w = z then {u,v,w} is a system of coordinates vanishing at (1,0,0) then 1 ? 2x + x2 ? yz2 = (1 ? x)2 ? yz2 = u2 ? vw2 is written in the canonical form.

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