WHAT IS WHOLEMOVEMENT?
Wholemovement comes from the word geometry, which means "earth measure". The earth is spherical; the sphere is the only form that is inherently Whole. Measure is movement from one location to another. Comprehensively the word geometry means Wholemovement. We need to update our vocabulary to better reflect our current experience and understanding since we have traveled from the earth and are now measuring the universe unknown ten years ago. The movement of the Whole is an inclusive, transforming self-referencing system. There are endless parts within divisional movement of the Whole.
WHAT DO YOU MEAN WHOLE?
The Whole is all we know that is, and all we will never know of what is. One nine year old child said, It is something you can not add anything to or take anything away from. The Whole just is, because there can never be a sum to endless generation of parts. When we are thinking parts our focus is shifted away from what is Whole. Geometry is only a part of the inclusive nature of the infinite self-referencing Whole.
WHY IS FOLDING CIRCLES IMPORTANT?
The circle is not the image we draw. The circle is a compression of spherical unity to a flat disc in space. Folding the circle decompresses and replicates 3-D formations and the 2-D distortion of compression formed in the folded creases. The circle is comprehensive to pattern, generating forms and complex systems in space where every part is within the context of all other parts. Everything is always in the context of everything else. The extensive information that is generated through folding the circle can not happen with any other shape or form. Calling the image a circle has prevented us from knowing the nature of the circle and exploring it further.
WHAT CAN I LEARN FROM FOLDING CIRCLES?
Everything is in the Whole of the circle and how much you learn depends on how much you observe, the connections you make, and what you discover that has meaning to you. All of the abstract generalizations of mathematical functions are demonstrated in observing what is generates in the folding process. All 2-D and 3-D shapes and forms are generated from the principles and patterns inherent to the movement of the circle. The richest learning is experienced within the greatest context, which gives value to the greatest meaning. There is nothing that concretely demonstrates the concept of Wholeness better than the self-referencing of folding circles.
WHY IS THE CIRCLE SPECIAL MORE THAN OTHER SHAPES?
The compression of sphere/circle unity can not be generated by any other shape, form, or constructed system. The circle can generate everything that all polygons do, but no polygon can do what the circle does. The Wholeness of the circle is just one thing, everything else is contained within the circle and is revealed by simply folding, sequentially one crease after another. The circle is simultaneously part and Whole; the contained and the container, all in-formation.
HOW DOES THIS HELP ME LEARN MATH?
It gives a hands-on experience of discovering generalizations and abstract formulation from observation and reflection about the forms and the functions generated by folding circles. Students have the opportunity to discover mathematics for themselves. The formalistic information found in math books is inherent to the circle and revealed through systematic folding. Everything is multifunctional and is in the context of everything else. It is easier to learn the abstracted functions of mathematics when observed and discussed in something as simple as folding a paper plate than it is to read somebodys interpretation of some abstract idea.
DID YOU DESIGN ALL OF THESE?
No I do not design the folding or combining of circles in any traditional sense. I pay attention to what the circle does, not so much to what I want to do with it. It is about observing and forming a dialogue with the circle. This is an exploration to find out the nature of the circle and what can be generated by simple folding and joining. It is about observation and paying attention to the symmetry of movement, allowing the forms and systems to develop, and they are always beautiful.
DO YOU COLOR THE CIRCLES BEFORE YOU FOLD THEM?
Not usually. There is greater design potential using the folds; they are fundamental to the movement of the circle. Without the folded grid there is no natural correspondent between the flat surface and the 3-D form. There is value in using circles with different colored sides or with preprinted images before folding. The unity of the circle and using the folded grid assures designing to correspond to all reconfigurations and symmetries. Using the grid to design effectively for a given reconfiguration can be a good challenge. Mostly I use color as information to track various arrangements and relationships of parts that are difficult to see otherwise. You may color as you wish.
ARE ALL FOLDS NECESSARY JUST TO MAKE A TETRAHEDRON?
When creases are dropped from the folded grid we are left with a formula that limits our understanding and the transformational nature of the circle. Without the supporting context we get stuck in separation and connections are lost. The folded grid not only forms the tetrahedron but allows many different transformations of the circle. The folded grid is the means of what you fold to connect to what was folded before, and to all that is yet to be folded.
IT LOOKS COMPLICATED, CAN I DO IT?
If a person can fold a circle in half they can do it. It is in the principled simplicity of the process, the unity of the circle that makes this an easy and accessible process, even to 4 and 5 year olds. No cutting or measuring, just reasonably accurate point-to-point folding puts the creases where they need to be.
I AM NOT GOOD WITH MY HANDS, CAN I DO THIS?
IT Understanding how to do this not difficult, even for people that do not work well with their hands. The understanding is in the doing , not in reading how to do it. The words and pictures only guide you into the experience, which is where the understanding is. Even people that are blind have been able to fold the circle into tetrahedra and octahedra, and understand what they have done.
GOOD FOR MY ADVANCED STUDENTS, WILL OTHERS GET IT?
Again, if they can fold the circle in half they will get it. Sometimes it is more difficult for accelerated math students to get back down into their bodies and fold because they are so comfortable with the abstractions in their head. It is good stretching for both advanced and slower learning students. This is a new understanding of the circle for everybody.
THE ART IS OBVIOUS, HOW DO I LEAN MATH?
Observation and reflection. The art is obvious to artist, the math is obvious to math people. The geometry form is the same and obvious to everyone weather understood or not. The circle shows one process with the same principles and patterns of formation. Different languages describe the same functional interactions between parts differently. Having folded circles there is an understanding of pattern formation and the interconnections that makes mathematics more understandable with a greater sensitivity to the beauty and efficiency of the language.
WHAT BOOKS ARE THERE ABOUT THIS?
To my knowledge there are no books, other than what I have written, that addresses the comprehensive nature of folding the circle. There are books about the circle as symbol, some about craft projects using the circle, some that use the circle to illustrate basic geometry vocabulary and isolated math functions. All of them are fragmented in approach and do not address the Wholeness of the circle, or even suggest there is more to discover in what the circle might be.
IS THIS DIFFERENT THAN ORIGAMI?
Most paper folding starts with a polygon shape. Origami uses square paper. The square is only part of a circle that has been cut into five pieces and four are discarded. This lacks economy. The circle has infinite diameters; the square has been reduced to two. Having no sides the circle has no limits. Most paper folding is about product, the circle is about process with endless product. The circle is comprehensive, and origin to all folded shapes and forms. Nothing can do what the circles does
HOW DO YOU JOIN CIRCLES?
In what ever way is appropriate for the system being developed. Attachment is a big part of problem solving in making models of any kind. Normally I use masking tape, hair pins, sometimes glue, twisty ties, paper clips, sewing connections with thread, or tying with string. Since this is an exploration everything is okay, with one exception, the circle is never cut. If you cut the circle you destroy unity and are back into limitations that come with working with parts in separation.
DO YOU HAVE A MATH BACKGROUND?
No, my background, training and interest is in art. I learned geometry on my own because I was interested in patterns of movement and how things are ordered, arranged, generate and transformed in space. Mathematics I have come to understand by folding circles, observing the number patterns reflected in the functions of folding.
HOW DID YOU GET STARTED DOING THIS?
Twenty-five years ago I took a class in geometry taught by Hazel Archer. We studied the work of Buckminster Fuller and that first day changed everything for me realizing everything we know about patterns observed in geometry, math, art, the sciences, and in nature, are all the same pattern and process of formation. It can be understood and demonstrated. After ten years of intensive exploration into geometry I realized all spherical order is compressed into a circle and can be decompressed by simple folding. Since nobody was doing anything but drawing pictures of circles, I then decided it was my job to fold circles. For the last sixteen years I have been folding paper plates exploring the nature of the circle and working with teachers and students at all grade levels.
THIS IS RELIGIOUS, DO YOU TALK TO STUDENTS ABOUT THAT?
Yes, when students bring it up. Keep in mind the circle is comprehensive, it is inclusive to universal patterns and principles of formation, therefore is reflected in all religious practice. Religion is deeply a part of the human consciousness that regards the unknown beyond our control and understanding. Not to consider this aspect of human concern is to disadvantage ourselves and deny our individual and collective potential as physical, mental ,and spiritual being of what is divinely beyond understanding. I do not talk about anyones religion, only the human need for some kind of faith in what is unknown and what it is that we experience and see in front of us.