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

```

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