When a surface has zero curvature over one of these, its Gauss map has a fold catastrophe.
When a surface has zero curvature over one of these, its Gauss map has a fold catastrophe. In polar coordinates, one of these may be specified by setting a constant equal to the product of r and one plus cosine theta, and Archimedes wrote twenty-four propositions about them in a treatise that found the area of an arbitrary segment of one, while averaging the midpoint and trapezoid rules gives the result of a numerical integration technique employing these. For 10 points, identify this curve featured in Simpson's rule, which may be defined as the locus of points equidistant from the directrix, a line, and the focus, a point, the conic section with unity eccentricity, also the graph of a quadratic equation.
When a surface has zero curvature over one of these, its Gauss map has a fold catastrophe.
{parabola}