Spin and the 120 LCD Spherical Triangle of Synergetics

In my previous post "Planetary Energetic Grid Theory" I talk about how various New Age philosophers have used the mathematically proven geometries from Buckminster Fuller's Synergetics to further their own pseudoscientific theories. I would like to delve a little deeper into this issue and point out the difference between New Age pseudoscience and real science.

I encourage the reader to review Synergetics section 901.00 Basic Disequilibrium LCD Triangle for an explanation of the relevance of the 120 LCD spherical triangle geometry to the modelability of nature's structures. Buckminster Fuller discovered these geometries as being generalized operational principles of Universe evident in natural structures. These structures appear on all scales from the micro-cosmic icosahedral protein capsid of a virus to the macro-cosmic spiral arm of a galaxy.

901.02 The Basic Disequilibrium 120 LCD Spherical Triangle of synergetics is derived from the 15-great-circle, symmetric, three-way grid of the spherical icosahedron. It is the lowest common denominator of a sphere's surface, being precisely 1/120th of that surface as described by the icosahedron's 15 great circles. The trigonometric data for the Basic Disequilibrium LCD Triangle includes the data for the entire sphere and is the basis of all geodesic dome calculations. (See Sec.612.00.)

See the website of R.W. Gray Projects on Great Circle and LCD Triangle Info for a very complete explanation of Bucky's concept of how the great circles are defined by spinning the polyhedron about an axis. He explains in great detail the derivation of the LCD Spherical Triangles and provides corrected tables of angles.

Image with Becker-Hagens copyright but contains diagrams from Synergetics

Note how the completely rational and mathematically derived 120 LCD Spherical Triangle model of Synergetics is compared in stark contrast to the plagiarized and emotionally derived UVG 120 Sphere by Becker-Hagens. It is interesting to see how Becker-Hagens copied exactly the drawings from Bucky straight out of Synergetics and added their own copyright to them. See "Illustration 17 - Planetary Grid Projection" compare with "Fig. 986.405 Respective Subdivision of Rhombic Dodecahedron (A) and Rhombic Triacontahedron"

Synergetics Fig. 986.405 Copyright © 1997 Estate of R. Buckminster Fuller

We all realize that the images of geometric forms discovered by Bucky's brilliant and extraordinarily disciplined mind are potent in their beauty and resonate on many levels of the psyche due to their intuitive connection to the coordinate system of Universe. The lesson here is that we need to be careful that these images do not become symbols and signs of a new religion which removes the images from their rightful place at the heart of the Design Science Revolution.

Geometry is a true science that can lead humanity to innovations which use less resources to accomplish more benefit for Humanity. The magic and mystery resides in the ability of the Human mind to derive the generalized operating principles of Universe from experience and observation. However, the geometric images in of themselves do not possess magical properties to divine the source of etheric energies beyond that of inspiring within the seer the motivation to use their own internal creative energies for the betterment of the planet.

Spirals: Geometry Of Awareness

If you have visited my website http://www.karmatetra.com/ you may have noticed that I am fond of spirals. What is it about spirals that evokes the imagination? The Golden Spiral has inspired philosophers, poets, architects, physicists, astronomers and biologists. We see spirals in nature; from the recorded trails of exotic subatomic particles, to flowers and galaxies. Spirals are everywhere.

Recently, I have been exploring spirals on the surface of spheres. I have published a study on generating these spirals on my website. See Spheriphor Study 03 for details and images. As far as I know this is the only spiral of its kind. There must be other people who have created a geometric design where spirals symmetrically cover the surface of a sphere - so if the reader knows of any, please comment here and let me know where they can be found.

I do a lot of my work in POV-Ray. I have provided sample code on my website for generating some of the images. I even provide information on how to run the code. If the reader is willing to follow a few step-by-step instructions, then it should be fairly simple to reproduce the images.

The image shown in the beginning of this post is titled Golden Spiral Sunset Sailing. It is a 3D rendering of a series of rectangles arranged whimsically in the space above a tranquil body of water. A spiral reminiscent of the Golden Spiral flows through the rectangular structure like the sails of a fanciful sailboat. More spiral digital art to come in future posts ...