System of Matrix (1)

Status of most elemental unit

This figure by 8-circles is the most elemental unit of the matrix that relics covered by this investigation depend on.
The actual used matrixes that exist behind most relics covered by this investigation, which are variable compositions consist from this minimal element.
The fundamental behavior of this construction is the method to build up pentagram that is an appearance from entirety of geometry.

It is better to consider only circle's alignment without central axis, for easy grasp..
The circle's size of this figure are only two.
Those are grouped [small-horizontal-3-circles posited in middle]and [opening large-radial-5-circles to outside].
In order to grasp as easy as possible the entity of the matrix, divided 2 figures illustrating each 2 groups are prepared.

To decide those 3 circle's position, it is necessary to find points that quadrisect horizontal diameter of central circle.
Two same diameter circles of left and right are able to draw,
when those circle-center put on the found quadrisection points upon the horizontal diameter of the center circle.

If this composition is formed exactly, It is able to draw a equilateral triangle showing yellow line.

The emphasized circle in the next figure is put on as the same center circle of the upper figure.
In this figure, a pentagram is inscribed in this circle.
Then, radial-5-circles that each center-points put on tops of the pentagram and taking radius from a side of the pentagram are added.

In the actual drawing of the pentagram that is inscribed in a circle,
the process to put 5-tops on the center-circle line is necessary.
This step is concerned with the quadrisection of the horizontal diameter of the center circle,
to get the position of small 3-circles.
As this relation, it can understand that the upper 2 figures explaining each polygon drawing method
are according with consistency of geometric, in themselves.

It results in the status of the next figure combining the upper 2 figures.
And, The figure showing fundamental relating circles without all straight lines for the explanation
is placing at the top of this page, with only added center axis.

investigation by Yagihashi Tsukasa (jabrec-art-music)@2011jan 17