Thursday, 30 May 2013 10:26

Practical Application of Folding Circles

Inherent in the circle are structural forms and proportional relationships of many design possibilities for a wide diversity of products for the human landscape along with the obvious connections to a variety of geometric and biological forms. Often people come up to me and suggest I should make this or that idea that comes to mind from them looking at models of forms and systems generated by folded circles. My response is always “you thought of it so it is yours to do.” I do not develop specific product, that would detract from my job exploring the circle, a transformational process showing what is there that we do not know, to leave some record of the comprehensive nature of folding circles, the only shape that can inclusively demonstrates unity. The development of product I leave to others to explore.

A week ago Wyman Williams sent me a video of a wind generator he made from two tetrahedra. He calls it a TetraGen, a concept he developed from having attended a folding circle workshop about eight years ago and buying a book about the folding. I want to share his work so you can see folding circles does not have to be fancy or complicated to reveal potential for a practical, efficient, and economical solution to a serious global problem. He is developing a wind-powered generator simply and cheaply.

I will let Wyman tell you his own story:


       “One night in late 2012 is was using your book (Folding Circle Tetrahedra) as a guide to exploring folding the tetrahedron with circumference outside. It occurred to me that if the resulting material outside the tetrahedron were attached to three faces and stacked on another tetrahedron with the material arranged to catch wind like the one above, it should rotate around a shaft through to center. I folded and taped the tetrahedra and attached them to a shaft made from a coat hanger. It worked quite well in the wind.






I then built a more durable model out of corrugated sign board and aligned it in the same arrangement as the paper plate model. I attached it to a threaded rod and inserted it into two lawn mower wheels attached to the top and bottom of the base. It worked, but took a much higher wind speed to turn it than I had anticipated.






I bought a toy propeller wind generator kit and attached my improved arrangement of the tetrahedra made from poster paper instead of the propeller. Instead of matching the faces of the stacked tetrahedra, I splayed them into a hexagonal arrangement. You can see in the video it really works well.


I then restructured my outdoor model in the hexagonal arrangement. It now begins spinning at very low wind speed. This structure has been spinning outside for over five months and is still in good shape”.   - Wyman Williams -      



This generator design could not be stronger, lighter, or more economical due to the structural nature of the tetrahedron by using the entire circle. Without the circumference the tetrahedron would remain a regular solid polyhedron as traditionally defined. The circle reveals the tetrahedron to be a functional relationship  of the first fold of the circle in half; four points moving in space showing six relationships in a dynamic, structural pattern that is principle to all subsequent reforming and joining circles. The dual nature of that first tetrahedron is beautifully shown as Wyman forms two tetrahedra, relocating them around one of the seven major axis, finding advantage for the circumference folded to the outside.


Aside from the traditional geometry and mathematics generated in folding and joining circles there is a practical side to the process, as we have just seen. 3-D printing revealing new uses for reproduction and prototyping complexities, with an ever enlarging choice of materials, applications and design possibilities. It is important to retain a hands-on designing experience of the imagination that is not tied to computer design tools and programs, but that is structural and self-organizing by nature. The circle is purely transformational since nothing is added or taken away, as we do with all other designed forms of production. Folding requires the observation, imagination of the human mind, courage to explore, and the spirit of discovering unknowns that come from direct hands-on doing. With some of the extraordinary complex forms and beautifully individual expressions coming from traditional origami, there is nothing that will reveal what can be folded from within the circle. Only the circle has a circumference, which can be diminished to any number of sided polygon and folded to any polyhedral form. All reformations comes from the same folded grid matrix making it a truly unique transformational process where all folds come from a single source first movement. There are three possibilities of consistent folding in half, the ratio 1:2 that generates only three option of proportional grids; 3:6, 4:8 and 5:10 (these are discussed in previous blogs.)


There is much to be discovered by folding and joining circles that cannot be anticipated by drawing pictures or constructing preconceived ideas based on traditional adding parts or of taking away excess. I hope this makes the point that there is tremendous design potential in what is generated from folding circles that is not accessible using traditional ways of designing and modeling. While products that are derived from folding circles are an important part, they are not to take precedence over the experience of working with and observing the inner-connections between all parts in an inclusive and principled transformational process. The circle is the only form to demonstrate division generating a multiplicity of endlessly diverse units and systems starting with unity, where parts can then be added and subtracted.


Wyman has discovered the circle to be instrumental in stimulating new approaches to old ideas. I am interested to see what other people have developed by folding circles and what kinds of products might emerge. If you have pursued your own direction in folding circles I would love to hear from you and add you to a list of people exploring folding circles in directions I have not taken.





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