Overview on circle metric

There are many relations connected to structure of circles. Of these are some consisting of only circles, and other has to do with relations between circles and other quantities. In the treatise we will look at structures that goes back to circles and a special property connecting circles. From this property we will have types.

We shall look at tree different types of circle structures. The fist has to do with the apollonius circles, and a simple relation between their radiuses. This type has quite a few corollaries, and some morphological themes is present here.

The second type is the circle rings. These are structures of circles lying between to border circles.

The third type is the richest one, the ways of finding species here are nearly uncountable. One of these is the general relation between four circles.

General four

When one of the circles becomes a line, the relations is simplified. But still the general relation is complex. When the circles and line has special relations such as tangency and orthogonality, then the expressions are simplified.

Three circles and line

Here are the same special realtion, but now there are four circles.

Four circles

A special number relation has to do with integer Descartes formations.

Cube numbers

The Descartes formation is perhaps the most celebrated metric circle structure.

Descartes theorem

The Descartes formations can also have integer solution-

Descartes integer

A continuing of the integer Descartes formation, is the Apollonius gascet. Here an infinitude of integer circles is present.

Apollonus gascet