User:Dchmelik/Synergetics coordinates

Synergetics coordinates are various coordinate systems described by Buckminster Fuller's mathematics (SynergeticsR. Buckminster Fuller, EJ Applewhite. Synergetics: Explorations in the Geometry of Thinking.. Macmillan Publishers, 1975-1979, 2 vols., vol. 2, secs. 203.09, 986.205.) and later by Clifford Nelson.Clifford Nelson, '[http://library.wolfram.com/infocenter/MathSource/600/ Buckminster Fuller Notebooks]'. MathWorld, 2003. The coordinates are said to predate Fuller.

Types of synergetics coordinates

A synergetics coordinates system uses axes centred in a grid of one type of shape such as regular triangles or hexagonal packing of circles or spheres or others including in higher dimensions (some of which coordinates are only within or extending from the space of a finite shape, such as barycentric coordinates, and coordinates which may use multiple shapes in relation to each other (see Fuller's book or Nelson's pages showing Wolfram Mathematica graphics.)

Image:Tiling_3_simple.svg

File:Circle packing (hexagonal).svg

Examples

Regular triangular coordinates are a grid of equilateral triangles and of the form $(x,y,z)$ (see grid graph on right, as well as a hexagonally-packed circle-style coordinate grid.)

Notes

References

Stan Dolan. 'Man versus Computer.' Mathematical Gazette, vol. 91, no. 522 (November 2007,) pp. 469–480.
Urner, Kirby. '[http://wikieducator.org/User:KirbyUrner/Collaborations#Quadray_Coordinates Quadray Coordinates].' [http://wikieducator.com/ WikiEducator].
Weissten, Eric, W. '[http://mathworld.wolfram.com/SynergeticsCoordinates.html Synergetics Coordinates].' [http://mathworld.com/ MathWorld].

External links

Clifford J Nelson. '[https://web.archive.org/web/20121009041408/http://mysite.verizon.net/cjnelson9/index.htm Synergetics Coordinates].' [http://archive.org/ Internet Archive].

:Category:Coordinate systems