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For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.

A quadratic surface given by the equation x^2+2rz=0.

A fixed point of a linear transformation for which the rescaled variables satisfy (delta-alpha)^2+4betagamma=0.

A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus.

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.

A parabolic cyclide formed by inversion of a spindle torus when the inversion sphere is tangent to the torus.

A catastrophe which can occur for four control factors and two behavior axes. The parabolic umbilic catastrophe is given by the unfolding ...