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Buckminster Fuller Notebooks
Author

Clifford J. Nelson
Old MathSource #

0209-450
Revision date

2003-10-14
Description

R. Buckminster Fuller wrote the books, Synergetics, published in 1975, and Synergetics 2, published in 1979, where he uses the term "Synergetics 60 degree coordinate system". Bucky wrote that he discovered the coordinate system of nature in 1940, but his books don't give concrete examples of them.

The rational coordinate model for four-dimensional Synergetics coordinates is the regular tetrahedron “sitting comfortably” in the point lattice of closest packed equal diameter spheres.

The notebook SynergeticsCoordinatesDemo.nb demonstrates Synergetics coordinates and some applications: Bucky Numbers (fields essentially the same as the cyclotomic fields), Solving Matrix Problems Using Bucky Numbers, and Finding Roots Of Equations Numerically With Bucky Numbers.

The notebook TetraGlobe.nb uses the Synergetics coordinate system to normalize the globe to the surface of a tetrahedron, and the earth is displayed with the package WorldPlot as an unfolded tetrahedron (a triangle).

The packages RBFields.m and SynCoordinates.m are used for globally defined functions in the notebook TetraGlobe.nb, but the packages should not be used with the notebook SynergeticsCoordinatesDemo.nb.
Subjects

*Mathematics > Geometry > Solid Geometry
*Social Science > Geography and Cartography
Keywords

Field, Synergetics, Simplex, Buckminster, Bucky, Fuller, Coordinates, BuckyNumbers
Related items

*Bucky Number Mandelbrot   [in MathSource: Packages and Programs]
*Solving Matrix Problems Using Bucky Numbers   [in MathSource: Packages and Programs]
Downloads Download Wolfram CDF Player

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RBFields.m (4.3 KB) - Mathematica Notebook
Download
SynCoordinates.m (1 KB) - Mathematica Package
Download
SynergeticsCoordinatesDemo.nb (600.8 KB) - Mathematica Notebook
Download
TetraGlobe.nb (738.2 KB) - Mathematica Notebook