My Math Forum Traffic on regular lattice n-gons, polyhedrons

 Topology Topology Math Forum

 September 14th, 2016, 03:01 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory Traffic on regular lattice n-gons, polyhedrons If a square lattice (of 2d regular lattices) is most efficient for two-dimensional traffic, is a cubic lattice (of 3d regular lattices) most efficient for three-dimensional traffic?
 September 14th, 2016, 09:08 PM #2 Banned Camp   Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191 Do you have your definition/description of what "two-way dimensional traffic" is on a square lattice? Do you have the criteria for what constitutes certain two-way dimensional traffic having a greater efficiency than other two-way dimensional traffic, as they relate to a square lattice? These sound like highly specialized questions of yours.
 September 14th, 2016, 11:54 PM #3 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory "Two-dimensional traffic" takes place on a plane. One may move in any direction allowed by such a square lattice. __________ This is the best site I could find on the matter: Grids Are for Squares: 3 Reasons to Consider Alternatives for City Design | Sustainable Cities Collective They argue that rectangular (with fewer constraints than square) grids are the more simple, however not necessarily efficient for place-to-place travel. Think of our globe, with nearly rectangular areas near the equator, but convex triangular areas toward the poles. For greatest efficiency, one must keep to great circles. __________ I believe that rectangular symmetry can manifest the most right-angled configurations and match better with a plane surface. "Three-dimensional traffic," by virtue of its symmetry with rectangles, would share features of them -- simplicity, so-so efficiency, very good fitting, agreeing with other infrastructure etc. 2D and 3D rectangles work well from large to small scale construction. There is no single approach that can work for practical traffic engineering; one must compromise somehow. Rectangles seem to work well, and they share many qualities with a rectangular cuboid (3D rectangle).

 Tags lattice, ngon, ngons, polyhedron, polyhedrons, regular, traffic

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post xmas355 Algebra 5 February 11th, 2015 02:06 AM xmas355 Algebra 2 February 8th, 2015 03:02 PM mathbalarka Algebra 8 June 27th, 2013 06:49 AM probiner Algebra 2 January 19th, 2012 04:41 PM 1101 Algebra 0 March 8th, 2011 12:21 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top