Synergetics Coordinates NoteBooks

*To*: mathgroup at smc.vnet.net*Subject*: [mg32216] Synergetics Coordinates NoteBooks*From*: cnelson9 at gte.net ("Clifford J. Nelson")*Date*: Sun, 6 Jan 2002 03:38:33 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

The files SynC.cwk and SynC.word6 at: http://homepage.mac.com/cnelson9/FileSharing3.html have an explanation of Synergetics coordinates as AppleWorks 6.2 and MicroSoft Word6 word processor files. I can't read the Word6 file. Can anybody read it with the graphics in it? Cliff Nelson I wrote: The plane can be tiled with squares, equilateral triangles, and regular hexagons. There are two unique perpendiculars to the mid points of the sides of a square, three unique perpendiculars for the triangle, and three for the hexagon. The triangle and hexagon are both the same in that respect. So, there are only two obvious choices for coordinate systems, the square and the triangle. The square becomes the cube in three dimensions and the triangle becomes the tetrahedron. A mathematician might want to add this fact to: http://mathworld.wolfram.com/topics/CoordinateGeometry.html by doing a write up of the contents of "Synergetics Coordinates" documented in the Mathematica notebooks on MathSource linked to at: http://mathforum.org/epigone/geometry-research/brydilyum As far as I know, my version of the Synergetics Coordinate System is knew, but, it is obvious that R. Buckminster Fuller invented it and described it in his books Synergetics and Synergetics 2. The trilinear and quadriplanar and barycentric coordinates are different. Synergetics coordinates can be transformed to and from Cartesian coordinates very easily. They do not mention the "missing half" of the likely coordinate systems on their site. Cliff Nelson