Picture-3Wholemovement workshops are offered in a variety of ways, including classroom residencies with students, professional development with teachers, and work with home schooling groups. This process is accessible and relevant to students of mathematics, the arts and for all ages from first grade through collage level.

Workshops have been offered in both public and private schools, sometimes with teachers from different schools through District-wide workshops. We also offer library-sponsored workshops for children in local communities, special Math Days, family participation events connected with schools, as well as government outreach programs.

The workshops range from a half day to five days in length. Fees are $800 a day ($400/ half day) plus travel expenses. Materials are included.

Workshops are arranged to meet individual school needs, sometimes with teachers only, and other times only with students. Some workshops combineboth students and teachers. Art teachers get a lot of math, and math teachers get a lot of hands-on art. The patterns, principles, and functions are the same regardless of the form of expression. The folding process is the same for all workshops. The amount of folding and the information will change depending on length of time, specific level and interest of students, and the needs of the organization or school. See below for workshop discription and outline.

Course Introduction

Folding the circle is a comprehensive way to model the principles, patterns, and a transformational process foundational to understanding geometry and mathematical functions. Through systematic folding, reconfiguring, and joining circles, levels of information are generated revealing traditional shapes, forms, systems, and complexity, as well as transformations not seen in other form of modeling or construction. The dynamics of the circle in space is explored beyond what can be imagined from drawing image. Two and 3-D information is simultaneously generated by folding the circle without any prerequisite knowledge. This is a simple process where folding can be done by students starting at 4 and 5 years old. This is a new approach to understanding the circle for students of all ages.

Course Description

This is an interdisciplinary exploration of pattern generation and transformation. We will learn the principles, patterns and functions basic to spatial organization reflected in geometry, mathematics, the arts and sciences through a hands-on experience of folding and joining paper circles. Masking tape, hairpins, and paper plate circles are used. Participants will explore folding circles with a new understanding towards modeling, observing and reflecting about what is generated and talking about what we do. This process is about the Wholeness of the circle, looking for what we do not see, exploring what we do not know, and making connections to what we do know. Through hands-on discovery about the nature of the circle we find greater meaning in the 2-D compression of information by abstracting generalizations from 3-D functions. The demonstration and observation of the principles and pattern inherent to the circle are relevant to all areas of understanding.

Course Objectives
  • Understanding principles come first and are fundamental to identifying and interpreting all subsequent forming of information and development of spatial systems.

  • Using the circle as a direct modeling tool for presenting formulas and generalized mathematical abstractions of universal functions.

  • Familiarity with traditional polyhedra as pattern to formation; truncation and stellation, the in and out movement of connections between systems.

  • Understanding the importance of spherical order as structural pattern, and the systematic development and categorizing of traditional polyhedra.

  • Find benefit in the comprehensive nature of the circle as a dynamic transformational Whole unlike all other shapes and forms.

  • Experience the simplicity of folding circles, the depth of information, and the richness and beauty that can be generated through multiple joining.

  • To demonstrate observation that supports analytical skills, problem solving, crucial thinking, and self-learning. Folding circles is a natural feed-back system for developing accuracy in hand-eye coordination, and connections through inclusive thinking.

Course Outline
  • Difference between circle and image of circle.
  • Principals fundamental to spatial organization in first fold.
  • Observation of functions common to geometry, algebra, and art.
  • Platonic Solids, pattern directives to spatial organization.
  • Generalized formula and theorems in-folded to the circle.
  • 1:2 ratio is fundamental to all proportional development and symmetries.
  • Developing frequency division of the 3-diameter triangle grid.
  • Transformation of pattern through movement and change of form.

Target Audience

The focus is towards primary and secondary school math and art teachers, teacher education, and home schooling parents. Folding circles is new to everyone and builds a broad experiential foundation for understanding and interpreting patterns that have universal importance. The process is the same for all grade levels and is only different in presentation to the general level of class understanding. Being able to fold a circle in half is the only prerequisite. It is cross disciplinary and the only comprehensive, hands-on learning tool we have, and we do not know it yet.


Picture-1Since 1980, sculptor Bradford Hansen-Smith has been exploring geometry and patterns of spatial organization. His ongoing work involves understanding the inclusive nature and Wholeness of the circle. After ten years of exploring traditional geometry, he began to question our traditional understanding of pattern, principles, process, organization, transformation, interconnections, and the ways we have come to understand and teach geometry, mathematics, and the arts. Observations about ethical implications in the circle open philosophical areas equally as important as the mathematical information or aesthetic beauty. Hansen-Smith writes:

For eighteen years I have been folding circles , teaching this approach to students and teachers, in geometry and art, from primary grade up through college level. I have received three US Patents on transformational movement systems and published five books about folding the circle. Now my sculpture is all folded circles. I call folding circles the geometry of Wholemovement.

The question was recently asked by an Assistant Professor from the Malaysia Institute of Technology at the International Conference for Mathematics Education into the 21st Century; "Is Wholemovement a revolution or evolution in mathematics education?" I can only say that revolutions are short with intent to replace the old with what seems new, always a messy business. Evolution is longer and builds on what is already in place, expanding understanding, enlarging context without removing anything of value.

For scheduling questions and specific information about workshops please contact us at: This email address is being protected from spambots. You need JavaScript enabled to view it.