Skip to topic | Skip to bottom
Hiaz.EinarThorsteinnr1.1 - 28 Mar 2006 - 15:33 - TWikiGuesttopic end

Start of topic | Skip to actions

Einar Thorsteinn

Quote 1:

If one gets the hang of geometry, there is no way back. And to seriously study geometry is an irreversible decision to make.
I dont know how many years I have spent in this pursuit - when I could have been playing golf or washing my car... - but I tell you, I do not regret one second of that time.
One side effect of such a study is the discovery of how surprisingly regular and harmonic the world of polyhedral geometry is. In my opinion, these pure mathematical laws expose to us once more that the universe is a "planned phenomena". And also reminds us of the fact that polyhedral forms are probably the only cultural forms in the visible universe that every possible extraterrestrial culture will know as the same. These 3D geometrical forms are therefore culturally independent.
It would seem that for a first understanding between our world and other universal citizens, polyhedral geometry would be a good issue to present.


Quote 2:

Introducing the F.A.N.G.
Fivefold Symmetry
All Space Filling

The research effort in 3D geometry behind the Space Fang Space art exhibition, concerns a new definition of so-called fivefold symmetry space or “5S-Space”, one version of a geometrically or mathematically defined space. This has basically to do with one polyhedral form and the system it presents, by its exclusiveness to pack space all by itself in such a way, that no holes or rest volume is left. Therefore the “All Space Filling” definition above.

In order to understand this better, we can compare this form to the cube, which, as everyone knows, packs fourfold symmetry space, “4S-Space”, in such a way that there are also no holes left. We just have to look ouside our window, at our city or town, to realize this, then our culture uses the cubic form extensively because of this practical aspect.

It follows that the three axis-lines of the cubic form or cubic space that we generally call alternatively: east-west, north-south and up-down, are easy for our brain/ mind facility to understand and consequently to orient ourselve within. This is another great advantage of the 4S-Space definition.

With the FANG and its place in the 5S-Space, this is more complex, however also understandable to us, once we have been introduced to this new definition. But we can also say that these two different polyhedral forms represent two different space realities. And we could even go as far as to theorize that on another planet in the visible universe, there is used this 5S-Space definition and not the cubic one. Then more degrees than just 90°degrees as here with us, become interesting on a general level, and therefore every school “out-there” would have a Degree Box for reference. A Degree Box would be a household word in that reality.

The packing aspect of both the cube and the FANG makes both of them fractal forms in the sense that when they are either multiplied and added together or cut down into smaller pieces and unpacked, they themselves can be/ are formed again in certain steps. The FANG works the same way within 5S-Space as the cube does in 4S-Space. They are the only two known forms that fulfill these two conditions:

  • 1 not only packing space with one form, but
  • 2 reproducing themselves at some steps of the packing/ unpacking process.

But why would this be interesting to us now? Is it not just a mathematical game, anyway?

Well, it so happens that nature uses both the 4S- and 5S-Space systems to build its so-called self-organization forms with, for instance natural crystals. We are well on our way in understanding how the 4S-Space part works, but not so with the 5S-Space one. Now, only 21 years have been spent on this research in the field of Quasi-Crystals with some results but not the final ones. Therefore the FANG definititon of 5S-Space and its eastetical aspects presented by the Space Fang Space exhibition, are very actual part of our present cultural reality.


Online resources:

to top

Hiaz.EinarThorsteinn moved from Hiaz.EinarThorstein on 14 Apr 2005 - 15:06 by HiazHhzz - put it back
You are here: Hiaz > CategoryGeometry > EinarThorsteinn

to top

Copyright © 1996 - 2006 by hiaz. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback.