Folding circle Terahedra: Truth in the Geometry of Wholemovement
by Bradford Hansen-Smith
Prefect bound, soft cover, black and white illustrated, 390 pages
Wholemovement Publications, Chicago IL, 2005
ISBN# 0-9766773-0-x

BUY ONLINE AT FoldingCircles.com

TABLE OF CONTENTS

Preface

Introduction

GENERAL INFORMATION

  • Using this Book
  • Principles
  • Wholeness
  • Biggest picture
  • Sphere and circle
  • Pattern, form, design
  • Vocabulary and function
  • Folding circle in half: touching points
  • Straight line, right angle and pi
  • Points, lines, planes, numbers
  • Fibonacci series
  • Golden ratio
  • Drawing circles
  • Diameter
  • Branching
  • Letters and numbers
  • Pythagorean theorem
  • Suggestions for primary grade level teachers
  • Assessment

    • MECHANICAL SUGGESTIONS

  • Creasing, Taping,
  • Hinge joint, Glue, Hair pins
  • Stringing points, Tying, Coating and Painting
  • Ways of joining
  • Coloring

    • 1. FOLDING THE CIRCLE

  • One diameter first fold
  • Three diameters
  • Exploring three diameters
  • Discussion: three diameters
  • Thinking algebra
  • Degree in a triangle
  • Folding the sphere
  • Spherical matrix
  • Collapsibility of the sphere
  • Discussion: vector equilibrium sphere (VE)
    •

    2. FOLDING THE TETRAHEDRON

  • Discussion: tetrahedron
  • Helix, loops, and spirals
  • Discussion: polygon
  • triangle
  • quadrilateral
  • pentagon
  • hexagon
  • The circle as compass
  • Sphere, circle, cylinder, cone, tetrahedron
  • Circle grid
  • Fractals
  • Frequency
  • Discussion: frequency
  • Opening tetrahedron
  • Joining open tetrahedra
  • Tetrahedron net
    •

    3. OCTAHEDRON

  • Discussion: octahedron
  • Multiple octahedron
  • Two-frequency octahedron
  • Octahedron face joining
  • Discussion: octahelix
  • Octahedron net
  • Open variations
    •

    4. ICOSAHEDRON

  • Net variations
  • Discussion: icosahedron
  • Discussion: 3 platonic solids
    •

    5. DUAL POLYHEDRA

  • Stellate & string tetrahedron
  • Stellate & string octahedron
  • Stellate & string icosahedron
  • The five platonic solids
  • Tetrahedron family circle
  • 13 Archimedean semi-regular polyhedra
  • Symmetry
  • Spiral
  • More about the spiral
  • Euler's formulas
  • Triangle matrix
    •

    6. TRANSFORMATIONAL SYSTEMS

  • Tetrahedron ring
  • Tetrahelix
  • Tetratorus
  • Tetratorus Mobius
  • Transformational net
  • Benzene ring
  • Discussion: benzene ring
  • Open stellated tetrahedron
  • In/out tetrahedron
  • Collapsible cube
  • Discussion: collapsible cube
  • Transforming triangles
  • Transforming octahedron / ve
  • Transforming Icosidodecahedron

    • 7. TETRAHEDRON INSIDE OUT

  • Circumference folded out
  • Spherical rhombidodecahedron
  • Rhombic torus
  • Inside out octahedron
  • Open close tetrahedron
  • Transforming rhombidodecahedron
  • Tetrahedron progression
  • Discussion: tetrahedron progression
  • Truncated tetrahedron
  • Discussion: truncated tetrahedron
  • Truncated cube
  • Discussion: truncated cube
  • Cube packing
  • Tetraspiral
  • Inside out dodecahedron

    • 8. SOFT FOLDING

    9. POCKET POLYFORMS

  • Discussion: soft folding & pocket polyforms
    •

    10. OTHER SYSTEMS

  • Collapsible tetrahedron
  • Five hinged tetrahedra
  • Transforming tetrahedron
  • Discussion: square prism / tetrahedron
  • Octahedra joining
  • Sliding edges
  • Discussion: sliding edges
  • Inscribed hexagon
  • Discussion: folded hexagon
  • Reforming the spherical VE
  • 12 point tetrahedron star
  • Triangle prism star
  • Square anti-prism star
  • Twisted tetrahedron
  • Twisted cube
  • Rhomboid
  • Discussion: rhomboid
  • Mobius surface
  • Soft Mobius
  • Discussion: mobius surface
  • Three looped Mobius
  • Bird
  • Photographs, drawings, and last word