Paper Plate Education
"Serving the Universe on a Paper Plate"

We recommend you visit Bradford Hansen-Smith's pages at www.wholemovement.com

Explore the work of Bradford Hansen-Smith  

·        The circle

·        Geometry

·        History

·        Requirements/materials

·        Folding circle in half

·        Principles

·        Folding 3 diameters

·        Make a sphere

·        Make a tetrahedron

·        Make an octahedron

·        Make an icosahedron

·        4-frequency diameter grid

·        8-frequency diameter grid

·        4 and 5 diameter fold

·        Books

·        Photos of models

·        Contact

The circle

The paper plate is a circle. The circle is fundamental to everything we know. Consider that we have drawn pictures of circles for over two thousand years. To get information from this static image we’ve had to invent sophisticated construction methods, using parts of circles (points, arcs and straight lines). The circle is just one of endless shapes used in art. In philosophy it is a symbol for everything. In math it is zero, a symbol for nothing. The image is used for many diverse purposes, representing ideas and concepts of all kinds. Practical uses of the circle have been excessively explored. We know very little of the information held within the circle.

The nature of Wholeness is demonstrated in the circle shape. The circle in space is dynamic, it moves and can generate information in a way not other shape can do. Countless forms and endless systems of spatial complexities can be made by folding and joining circles. This process reveals fundamental 2-D and 3-D mathematical information through divisional movement without separation. The patterns and formations of interrelated systems that come from reconfiguring the circle are the same as those observed in natural phenomena, pattern source for all areas of human understanding. 

This approach to the circle is spatial, a concrete forming of patterns. Complexities of transformational movement systems are developed from a simple, sequential process of folding. It shows forms changing one into another. Complexity of form is a function of the circle in multiple reflection, generating things that would be very difficult to model in other ways.

Geometry

The word geometry means earth measure. “Geo” means earth, the earth is spherical. The sphere is the only form we know that inherently demonstrates the concept of the Whole. “Metry” is about measure, intervals of movement between any two locations. The word geometry then comprehensively means Wholemovement, movement of the Whole to itself. Context is what gives meaning to anything. The greatest context gives the greatest meaning. The greatest meaning of geometry is then Wholemovement. The greater context of the circle is the sphere.

The circle is a compression of the sphere to a flat plane.  The sphere does not lose anything, it is simply compressed, reformed to a circle disk in space. Through the folding movement of the circle all spherical information can be retrieved, unfolded if you like.

We all started from a singular spherical egg cell. Through division of this singular sphere we came into this huge time/space sphere. Our experience is the movement between, the scaling of a spherical Whole beyond understanding. The circle is as large as it is infinitely small. That means the circle does not have a center, that is a scale function of concentricity. The circle is the center.

The Whole is self-referencing, nothing can be added or taken away. It can only generate and reflect, through movement, the wholeness of what it is. Many paper plates are used, each  reflecting the other. The paper plate circle is never cut. To cut the circle is to separate into parts, limiting ourselves to individual boundaries of endless fragments. This is also wasteful.

 History

Folding circles has no history. There are no references for folding the circle as a modeling tool or as a process for generating information. Most of mathematics is based on drawing pictures, using the circle to mean what ever we favor to think at the time. We continue trying to explain this  time/space location of movement patterns ordered to the Whole of what is, in abstractions drawn from static circle images that have been separated into parts and removed from their context.

The only historical reference I have come across is that in Japan in the late 30’s and early 40’s they were folding circles as well a squares. Somewhere in the history of origami lies the circle, unrecognized. The square and all other polygons are only a part of the circle, therefore limited to specific number of sides. The circle has no sides, it is without limit, without scale.

After ten years of intensive exploration into geometry, I realized everything we know about patterns are divisions into a sphere. The sphere compressed is a circle. Nothing of the sphere is lost. How then to reveal it? I have been folding paper plates for twelve years decompressing information. I find new things all the time. Students show me new things. It is an endless process.  

Requirements/materials

There is no age or educational experience required. Any one who can fold a paper plate in half can do it, from 5 years old on up. Paper plates, masking tape and bobby pins are used. There is no cutting or measuring, only proportional folding of the circle. Coloring is another activity requiring markers or paint. Glue can be used before taping. When glue is dry, remove tape. Be as accurate as possible when folding points together, lines will then be in correct place. Simple.

Folding circle in half

Unity is not broken by folding the circle. Any two points on the circumference of a circle, (imagined or marked) when touched together will fold the circle in half, forming two new points on the circumference, 4 points total. The diameter is perpendicular, half way between the direction of movement of the two points. By this action of symmetry a tetrahedron pattern is formed (4 points in space is a tetrahedron pattern; 3 sets of 6 edges where opposite directions are at 90° to each other) This right angle triangulated movement is principle to all pattern formation. It happens first. This first movement shows a ratio of 1:2, one Whole (singularity) in two parts. It models the tetrahedral pattern of Carbon, indicating the importance of this pattern as structural to the endless development of life formation.

Principles

What happens first? What are the qualities of this first movement? We start with the Whole of the circle. Through self-referential movement a division occurs revealing duality that takes the form of triangulation where each aspect is consistent to the movement of the whole, and each individual part is interdependent to the Whole, which then determines the interrelationship between parts. I call these qualities principle. They are primary to everything else the circle will do. They are principle directives reflected in all movements and in all parts of the circle. What we determine to be principle is the most reliable guide we have to direct our intentions beyond the conditional mind. Others may interpret different qualities in that first fold. I have taken what I find to be the most general, the biggest things that can be talked about. The greater understanding of what is principle reveals the greatest potential for meaningful action.

Folding 3 diameters

A.     Fold circle in half.

B.     Fold one corner point over making 2 equal  parts. Don’t measure, use your eyes to see the proportions correctly. Our eyes are a proportional feed back systems designed to do just this type of thing. Use them.

C.   Fold unfolded part behind and even up points and edges. Crease only when the edges, points and circumference are even. One fold on top, in middle, and one on the bottom, like a “Z”.

D.  This folds the semi-circle into thirds. Open to find 3 diameters.

  These 3 diameters are a hexagon pattern; 7 points and 6 intervals or spaces. It is a number pattern of 13 (7+6=13). One circle and three diameters. Geometry is all about spatial patterns, intervals formed by interactions of the Whole, creating endless movement that transforms time and space.

Make a sphere

A.     Bring 2 end points of one diameter together, hold them closed with a bobby pin. This forms a pattern of 4 tetrahedra; 2 tetrahedra and 2 tetrahedral intervals. Six points in space.

B.     Bobby pin 2 of these folded circles together in the same way, on the straight edges showing a square, or quadrilateral pattern that moves on perpendicular axis, reflecting first fold of circle.

C.       Join 2 sets of 2 together, straight edges joined with bobby pins. This makes a sphere of open triangles and squares, a Vector Equilibrium, traditionally called a cuboctahedron. There are 13 points of intersection reflecting the number pattern of the hexagon, of which there are 4 (1+3=4) circles, each starting with 4 points.