Oblique Circular Cones and Cylinders
Metric Geometry
2013-01-01 v2 Classical Analysis and ODEs
Differential Geometry
Abstract
Surface area and mean width of a cylinder (the convex hull of two parallel disks) in R^3 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?
Cite
@article{arxiv.1212.5946,
title = {Oblique Circular Cones and Cylinders},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1212.5946},
year = {2013}
}
Comments
16 pages