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Seven stars (continuation)

CHAPTER 7
(continuation of Chapter 6)

SEVEN STARS (continuation)

We will continue “searching” for new radii that emerge through the constellation of two radii – radius 3 (which divides the basic circle into three parts – twofold – a six-sided star polygon and each acquired part in the same way) and next to it the radius 7 (which divides the basic circle into seven parts – a constellation that forms a smaller six-sided star polygon that has again come forth from the poles and intersections of the hexagon) and precisely this seven is one of those angle magnitudes that are hard to draw. Why? Because with these “primitive” instruments of ours it is hard to draw one-seventh or 1÷7 = 0,1428571 or respectively one-millionth part of one whole. Thus, to a certain extent, the contemporary encyclopedists are correct when they maintain that it is impossible to construct a heptagon and nonagon circle only with a compass. Indeed exactness is impossible, but acceptable for the “state” in which present-day geometrical science persists due to the “crudeness” of the tools that it uses (say: the compass). The “witness” to this acceptability is the basis of our approach. The hexagon or division of the arc of a circle (the full angle by its radius or 1/6 = 1÷ 6 = 0,166666… To this very day it causes a problem to many and therefore they assert that ancient had no cognition of the zero. On the one hand, this is a strange assertion, for had they studied the legends of the Bible with greater attention (The Exodus, and Book of Numbers and the Genesis according to Abraham in the First Book of Moses), where it speaks of tenths and of the tenth part of one tenth (the tenth part belonged to Moses and the Levites and they bestowed the tenth part of one tenth to God). Therefore, had they more attentively studied the ancient legends and had better knowledge of the principles of mathematics there would be no need for unnecessary discussions, in the same way that our present-day millionth or ten-millionth part is unnecessary and was then, the same as now, rounded off into some “acceptable” decimal (for example like the number Pi) since the absolute zero (nil) is decimally far away, thus the base is number one and the rest are parts of one so that the theory of a negative number is indeed “strange”. And this should also be something to think about for those in search of the “anti” since it simply does not dwell in existence or, to put it mildly, “is too far away”.

But let’s go back to the “seven stars” constellation and partially explore the clean-cut radii – the new data that they “render” to us, and once again as “exactness” is concerned I’m sure that the future of civilization will thanks to its technological progress soon solve this issue.

* * *

With the construction of a smaller star polygon (seven of six from the basic circle and intersections of the divisional circles) we have acquired its peak poles. We circumscribe the radius of these poles with a circle.

* * *

This radius divides the basic hexagon circle (the circumscribed star hexagon) into 14 sections (making use of only two subtended poles of the basic circle – inscribing the division only on the arc of the basic circle and inside of it).

* * *

Its other intersections likewise (closer to arc of basic circle) and circumscribing them with their circle.

* * *

That radius divides the basic circle into 44 sections (again we use only two subtended poles), and two divisions – the two radii steers us towards the Pi number.

* * *

Circumscribe a circle around the internal intersections of the same constellation.

* * *

This radius divides the arc of its basic circle into 54 sections or 9 x 6, or 3 x 18, or 2 x 27 etc.  

* * *

Now we will put to the test one external intersection of constellations 7 and 3 with a circumscribed circle.

* * *

This radius divides the basic circle into 18 sections and forms the first nonagon star polygon (2 x 9 = 18).  

* * *

We move further on with one intersection of radius three (3 or 2×6) and radius seven inside the basic circle.

* * *

But let’s apply the system – internal radius – of circle from all 6 poles of the basic circle  or seven internal radii and internal divisional circles of the basic circle.

* * *

Inside the basic circle along with its arc we have acquired a “meeting” of all three radii in one point and we circumscribe this “get-together” of their radii with a circle.

* * *

This radius divides the basic circle into 33 sections (three poles were employed – every other one – logically from the subtended other ones  3 = 2 x 33 = 66 sections.  

* * *

We see that the internal circles of the constellation divide or intersect the arc of the basic circle at several points. We enter the span (radius) into the compass. The peak pole is one of those “passages”.

* * *

That radius divides the arc of the basic circle into five equal sections of which we have employed only one pole (peak), therefore the possible source of column number 5 (10, 15, 20, etc.).

* * *

But, perhaps we have gone too far. Let’s go back to the basics, the six-sided polygon of the basic circle divided by the divisional circles of same radius which we also circumscribe with the radius of the divisional intersections.

* * *

The circumscribed circle of intersections of the divisional circles with their radius is divided from one of the peak (intersections of the divisional circles) …

* * *

… with the same radius from all six poles of the basic circle…

* * *

… and same radius from the peak poles of the divisional circles, but only inside the basic circle. Thus we have constructed seven spherical six-sided star polygons with internal and external intersections (products of division in the manner of Sacred Geometry).

* * *

Let’s take just two external intersections, specifically intersections of the divisional circles and spherical sides of the six-sided star polygon. This is a radius that divides the basic circle into seven sections – from point to point of division from the peak pole of the basic circle.  

* * *

And the (external) radius of just the spherical intersections of the six-sided star polygon divide the basic circle into 4 equal sections (we occupied only two subtended poles) and since we are focused only on dividing the basic circle we have nothing much to say about the “products”.

* * *

We will therefore continue applying full combinations in the following chapters, with the aim of acquiring new divisional data or accordant data (since various modes lead to our aim). From the aspect of geometry this means – there is only a single circumscribed polygon of any division but more than a single star polygon, and all the more the greater the extent of the divisions of the circumscribed polygons.

This mode of constructing constellations of spherical polygons tends to carry away, tandems and tandems of intersections that we haven’t even touched , and each intersection – of course there are always more and more – „talks with its radius, with its data point” and then its full-circle construction (or partial) talks about the earlier ones. Nevertheless, everything is accordant even though it is relatively hard to hold on to a clear mind and perception. Therefore it is sometimes good to take a break and retain the basics, the fundamentals, without going into an overflow of divisions, for as I have remarked at the start – with our “primitive” tools (the compass) we are subjected to relativity. But one day this will happen, maybe soon, when somebody gets engaged in the creation and perfection of computer-simulation programs. At times I am sorry that such excellent pundits of my own generation or younger generation (among whom I certainly regard Bill Gates) have stopped employing their spiritually innovative potential and surrendered to the rewards arising from their initial efforts and labor. Unfortunately, that is also a part of our humankind. We should take as examples and imitate such creators that have engaged their existence in this life (from Moses, Archimedes, Pythagoras, Christ and countless others in this or other scientific and cultural disciplines) to continue and become the masters of their trade.

(to be continued)

Tomo Periša
HR – Rijeka – December 10, 2011

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