Oblique Circular Cones and Cylinders
Abstract
Surface area and mean width of a cylinder (the convex hull of two parallel disks) in R3 are computed. It is more difficult to obtain analogous results for a cone (the convex hull of a disk D and a point p). Oblique formulas for mean width, as well as those for mean curvature, are new. Let L denote the unique diameter of D whose endpoints are equidistant from p. We conclude with a question involving the plane that bisects the cone and contains p,L, as p varies. What is the minimum ratio of the smaller measure to the larger?
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