It is important to understand the origin and the properties of what we are working with. In this case the 3-D circle needs to be differentiated from the circle image we draw. The circle, the subject of the image, has spatial properties that are unique from all other 3-D forms. We need to observed the differences in properties between 2-D and 3-D if there is to be any clarity and understanding about each.

If we do not know the properties of what we are working with we do not know what it is or what to do with it beyond arbitrarily imposing our will that frequently ends up violating the nature of what it is, often being counter to expected results. Lack of understanding properties has proven over time to cause unforeseen problems. Properties of the circle set the foundation for all subsequent folding (see previous blogs).

This picture shows a circle and the image of a circle.

The circle originates through spherical compression. Both circle and sphere demonstrate a dual function as individual unit and unity simultaneously. The non-differentiation of spherical surface is transformed by a right angle movement to the direction of an centrifugally expanding circle that reveals a triunity of three circles

The image shows one circle where as the 3-D circle shows three circles, one on each side and a circle ring. (Think of an extremely flattened cylinder.) There are two edges where the three planes meet. There is an inside volume and an outside space. Three planes, two edges, two spaces; (3+2+2=7.)

The circle is a triunity of three interdependent circles that can not be separated one without the other. In order to conceptually take them apart unity is destroyed, being left with three abstracted, isolated, and imaginary units. The association of three anythings is a structural pattern and reflects unity. All number of units will never equal unity, for unity is always singular. Units is always plural and infinite in number. Three is the first active number and seven is the most possible associations of three.

One set of three (ABC)

Three sets of each individually (A) (B) (C)

Three combination of sets of two each (AB) (AC) (BC)

Drawing a diameter divides the image in two halves. When folding the circle in half the diameter changes the properties where instead of two semicircles on one plane there are six semi-circle planes; six half circles. While this make no rational sense using a 2-D model, it is observationally logical to the folded circle. The circle remains whole, retaining unity even as folded into six half circles. ( If we decided to count the two edge circles it would change the possible combinations of associations.)

There is no conflict between folding and drawing circles; they are two very different systems; one is an image/idea of the other. Knowing the difference in properties helps clarify some confusion and greatly expands our understanding of the circle. It introduces a new area of dynamic exploration that in no way denies the theoretical or 2-D mathematics that has been developed. There are well over a hundred relationships, functions, and math concepts in this one fold of the circle into six halves. This is not to suggest one is better than the other, but rather to understand the difference and benefits of both folding and drawing circles and the connections between them. We know the value of drawing circles but there is no precedent for folding the circle and that means we have no experience or understanding about it. Only through the direct experience of folding will we understand the difference.

Besides the information and the beautiful objects that are revealed by folding, it is fun, interesting and engaging. We have a prejudice of not wanting to have too much fun learning something we have already decided should be difficult; if it is serious we must work at it. We are at our most open to learning when we are having fun and engaged in what holds our interest and simulates curiosity. Long ago we decided that mathematically the circle as image is a symbol for nothing, a place holder to later be replaced by something of value. It is now time to look at the information value of the circle beyond the image and the mechanical advantage we find in using it.

The information and reformation possibilities by folding circles demonstrates we can no longer afford to disregard circle/sphere unity. Because we have not done it before is no reason to continue to ignore it. I am writing these blogs in an attempt to give some understanding about the importance of the circle and that it might possibly simulate you to want to fold the circle and to find out for yourself and discover things there to be observed, and connections to directions not yet seen.