Creation of Geometry

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Creation of Geometry

Full, solid description of the whole geometry which, in turn, claims  completeness and strength is contained by four ultimate, geometrically pure symbols, each standing on the edge of the possible. Beyond them the possibilities of geometry are exhausted. In the field contained by these four there are all forms: figures, letters and the transitions between them, and it is a great beauty because the source does not know errors.

Here they are – a circle, a stick, a point and two points.



In essence, these four are separated completely and are not similar – each to each, in pairs and all together between them. They themselves can not meet, leave their border areas. They are a static geometry. However, between themselves they form transitions – the possible geometries.

The picture contained by the four symbols is that rare occasion when the whole can be grasped at a glance and that is a feature of geometry and thus it comes first.

The four symbols are separated, their separation is demonstrative and perfect. It is the highest achievement of separation – it is a complete, comprehensive and obvious description of it.

About the circle and the stick (the world of non-interaction) there is nothing to be said. Their separation is absolute, it can not be discussed. They can not present it in description.

The four contain separated concepts but at the same time they form between themselves the possible geometries which have lineage.

A circle, a stick, a point and two points contain the picture of geometric static. All states of the Quaternary field as a superposition of the effects of the four ultimate symbols is a static – a single, non contradictory picture talking about the forces that occur at crossings, about the uniqueness of the form in these force fields in each concrete place.

The transition from one geometry to another in a static Quaternary picture is not a movement. However, these transitions may contain as an element the emergence of forms of motion. The movement in its possible forms in each particular place is described by a static picture and is also an element of static.

Static is a capacity, a substantiation, a right of existence of geometry – of a visual image.

For example:

The geometry between the circle and the stick is formed by the influence of the circle and the stick. Closer to the circle the circle’s influence prevails, closer to the stick – stick’s.

With the minimal shift from the circle in the direction of the stick appears a geometry of the correct polyhedron which retains influence of isotropy of the polyhedron. It is almost isotropic but consists of sticks, i.e. it satisfies the requirements of both – the circle and the stick. Drawing nearer to the stick the anisotropy increases and the number of faces of the polyhedron lessens all the way up to a square.


In the direction from the circle to the two points the circle loses closure and gets a rupture.


Enter a caption

The gap in the circle reveals to our eyes a birthplace of the great Grover washer on the Quaternary field. And at the same time it prepares us for the volumetric view of the world.

Further, being torn the circle can not retain its shape and continues to curl in. Moreover, its ends are not twisted identically: one of them tends to the form of a circle and the other tends to the one of the two points.


Closer to the two points this symbol breaks into two parts – a point and a comma.

Stick, experiencing the impact of the point, begins to break, gradually forming a broken line and near the point turns into a rounded comma. In the origin of the comma it’s possible to recognize both: a stick, rounded under the influence of the angle of rotation and a point to which a broken line tends.

The geometry of transition between the two points and the point is most difficult for representation. This is due to the fact that here reigns the idea of rupture. It can be said that in this sector of the Quaternary field are investigated the ideas of separation of the identical, the connection of the different ones and the change of the quality of the interval between them.

This “run” of the Quaternary field barely allows to review a harmonious coherence of the forces standing behind a visible image.