From: David Eppstein Subject: Re: Pick's Theorem on Volume Date: Fri, 20 Oct 2000 22:45:01 -0700 Newsgroups: sci.math Summary: [missing] In article <8sr8qt$foc$1@bob.news.rcn.net>, "Hamilton Davis" wrote: > Can a variation of Pick's theorem be applied to the volume of a polyhedron? Not directly -- there are tetrahedra with four lattice vertices, no other interior and boundary lattice points, and different volumes. However there are apparently some connections between higher dimensional Pick theorem generalizations and toric varieties -- see http://www.ics.uci.edu/~eppstein/junkyard/pick3d.html for a couple pointers. -- David Eppstein UC Irvine Dept. of Information & Computer Science eppstein@ics.uci.edu http://www.ics.uci.edu/~eppstein/ ============================================================================== From: "Vladimir Lazic" Subject: Re: Pick's Theorem on Volume Date: Sat, 21 Oct 2000 19:44:36 +0200 Newsgroups: sci.math A sort of, yes! Generalizations of Pick's theorem were delivered by Reeve (for the 3-dimensional case) and Macdonald (in general). See: 1. I. G. Macdonald, The Volume of a lattice polyhedron, Proc. Camb. Phil. Soc. 59 (1963), 719-726. 2. J. E. Reeve, On the volume of lattice polyhedra, Proc. London Math. Soc. (3), 7 (1957), 378-395. 3. J. E. Reeve, A further note on the volume of lattice polyhedra, J. London Math. Soc. 34 (1959), 57-62. Hamilton Davis wrote in message news:8sr8qt$foc$1@bob.news.rcn.net... > Can a variation of Pick's theorem be applied to the volume of a polyhedron? > >