of countless parts and systems generated within the movement of Whole circle/sphere unity. To fold circles is a dynamic process; practical, informational and a hands-on way to integrate “holistic thinking” into a functional worldview that demonstrates principles common in all pattern-based understanding. Folding circles requires the least input for the greatest output of all methods of modeling and information generation. We don’t know this, we do not fold circles, nor do we look for information inherent to the circle as both Whole and part.

Reassessment of the circle as Whole is a necessary trimtab that will move us towards discovering a balance between separation and fragmentation of parts to the co-ordinate differentiation of Whole circle functions. Folding and joining circles demonstrates the structural nature of a self-referential, principled, information generating, inter-transformable, nothing added, nothing taken away, comprehensive movement system.

One cannot anticipate from pictures of circles, the amount or kind of information generated through systematic, sequential folding and joining. The contextual Whole gives value to meaning of what we know, as well as unexpectedly revealing much we don’t know. With serious consideration, folding circles can help alter our perception about the nature of the universe and broaden the parameters of mathematics. The circle is both Whole and part, thus indicating direction for the development of human potential towards becoming meaningful cosmic participants.

As symbol-making animals we use the circle image primarily representing nothing, zero. The image is not the thing represented. The sphere is the only inherently undifferentiated Whole; origin to all polygons, polyhedra, organization, and arranging of life forming systems. Through right angle compression the sphere is reformed to a circle disc without destroying spherical unity. Through folding the circle, spherical information, 2-D distortion, and all mathematical functions are decompressed in replication, principled to circle/sphere Wholeness. Folding circles reveals principled patterns fundamental to our perceptions about origin and observations about evolving processes, particularly instructive to mathematics, arts, and science education.

Demonstration
Fuller folded four paper plates, three diameters each, edges touching, making a spherical VE. That one demonstration revealed to me that everything could then be modeled by a simple and sequential process of folding and joining circles. I began to explore folding paper plates to find out how much and what kind of information, and reconfigurations are generated through Wholemovement of the circle.

The circle/sphere is origin-base to all geometries, mathematical functions, all design probabilities, including all “comprehensive anticipatory design science” imaginings. Eighteen years of folding circles support this claim, with nothing yet to disprove it. Anyone observant to what happens with folding the circle in half will be able to describe any number of over fifty fundamental mathematical functions that occur in that one fold. Folding circles is an effective way for young children, anyone, to learn by discovering mathematics for themselves.

Touching any two points on the circumference creates two more points. Two congruent areas when rotated around the diameter-axis-bisector-line of symmetry will form a spherical movement, simultaneously forming a tetrahedron pattern, indicating polyhedral direction of reformation. These patterns of movement are overlooked because we focus on images, static forms and formalized relationships of dynamic interaction. There is nothing arbitrary, ambiguous, or difficult about folding circles. All parts are multi-functional, interconnected, inner-transformable, informational, and infinitely aligned within the Whole of the circle/sphere.

Education
Through folding, the educational value of the circle becomes apparent, the beauty obvious, with ethical demonstration in the integrity of structurally patterned interaction between generations of unit parts and systems within the circle; not possible with any other shape or form. It is impossible to imagine the amount, kind, and depth of information, reformation and complexities generated, without first having experienced folding a circle.

Educationally and emotionally our fascination is with parts; we do not address Wholeness except as a local “holistic” concept. We accumulate, rearrange, and systematically construct fragments searching for value that can only be found within the nature of the Whole. Observing patterns, reforming, and transformations of inner-related systems within the circle gives demonstration allowing us to make connections that transcend the understanding of separation observed in static forms of modeling.

If the current generation of first grade children folded circles their experiential understanding of interconnections and Wholeness would change the meaning and value of knowledge gained in all other ways. Presently educators are stuck with fragmented information, varieties of separated materials, limited manipulative tools, with confusion about the nature of Unity. With simplicity of process and circle/sphere Wholeness all separations of information become unified in one inclusive place. Fuller demonstrated structural pattern is principle to all formation. The first fold in the circle shows qualities that come first; therefore, are principle to all else that follows in folding circles. These structural principles are observed throughout all life-forming functions.

There is no equivalent in traditional geometry or in other disciplines to the extraordinary transformational nature of the circle/sphere. The circle demonstrates things we do not know without violating anything of value about what we already know. The Wholeness of the circle reveals through folding what is otherwise not possible to see.

We have missed the circle as the most comprehensive, hands-on, accessible, educational tool we have because of our attachment to symbol making. There is no precedent for comprehensively folding and joining circles, no recorded documentation of in-depth study for information, except Fuller’s VE demonstration, and the books I have written about my exploration into this process.

Practical
You don’t have to know anything to be observant to the connections and multi-functional nature of what already exist as revealed, fold-by-fold in the circle. Students can discover mathematics for themselves through observation, reflection, and the stimulation of making their own connections. Everything the circle generates is always in context with everything else showing infinite symmetry with finite co-operation through appropriate interaction principled to the Whole. The circle is dynamic and gives functional demonstration to that which has been previously conceptualized through abstract analogies and in mathematical symbolic language. The potential of the circle is maximized with every fold through systematically touching points, with every reconfiguration of the circle revealing ongoing accumulation of options and design possibilities, where meaning and value of every part, and all information generated, is dependent on the purpose and movement of the Whole.

Circles are easier to fold than draw. Materials are minimum; paper circles, bobby pins, masking tape. It can be done anywhere by any one that can fold a circle in half. This shifts the focus from teaching to individual learning; to observation through direct experience and contemplation. The simplicity of the Whole and the principled patterns of folding circles cross all cultural and educational boundaries. Contextual understanding reveals information and relationships that are not found in our education curriculum. We are without experience about the profound educational effect that folding circles might have.

Dissemination
Getting as many people as possible interest in exploring folding circles, at least as much as we draw pictures of them, has been limited to my book sales, giving workshops, and working with children in classrooms. It is important to develop global awareness about the benefits of folding circles through educational conferences, publications, and extended contact with schools. Through non-profit groups, a network will be established for public information and professional education development through workshops, demonstrations, DVD material, and Internet instruction. Through observing students folding circles the educational benefits are clear, but long-term evaluation and assessment will be necessary to establish creditability in planet-wide, cross cultural curriculum education.

Imagine a standard K-12 mathematics curriculum, a DVD that comes with a stack of paper circles. The efficiency and economics of compressed information storage with experiential hands-on outcome is obvious. A step-by-step circle folding process, in historical context, enlarged to a cosmic perspective towards a Whole worldview, will by nature accommodate many ways of individual self-regulated learning, that can be adapted on many levels to a variety of teaching styles.

Children, teachers, and circles are far more than what we educationally think about them. Opportunities need to be established for teachers to learn, initiate and integrate folding circles, culturally assimilating an expanding worldview, already well seeded in the direction of “whole systems” and “holistic thinking”. This will require training people to partner with schools, with math, art education, and science resources, without added financial burden. Elementary training is key to integrating circle folding into curriculum.

This unique approach to the geometry of pattern formation remains unrecognized because the Whole, until now, has only been a concept without demonstration. It is crucial to incorporate folding circles as experiential understanding of Wholeness into our educational system, if we are to reform our thinking towards balance and health of individual and collective life functions on this planet.