2012/12/24 by Steven R. Finch, Finch, Steven R.
Mathematics · #33B15 #33E05 #51M04 #51M25 #52A15 #52A38 #53A05 (Primary) 26B15 #60D05 (Secondary) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.CA #math.DG #math.MG #msc:26B15 #msc:33B15 #msc:33E05 #msc:51M04 #msc:51M25 #msc:52A15 #msc:52A38 #msc:53A05 #msc:60D05
paper · pdf · doi:10.48550/arxiv.1212.5946
16 pages
arxiv created 2012/12/31 · arxiv updated 2013/01/01
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?