## Twelve Stars

CHAPTER 14

Creating a background for a dodecagon division of the base circle from the duplicated three radiuses – the basic „six“ and divisional „three“ (or, simply, from the bisectors, three is the radius of intersections of the bisectors that divide the base circle into two triangles from their two opposite poles and from there the semicircles to the divisional perimeter that create radius “four”. Radius „four” divides the base circle into four parts, three times on the arc of the base circle creating 6 new poles and then from them we repeat all three radii to the perimeter thereby “creating” the background that provides the basic division and circles and background into 24 parts, yet it still gives the grounding for resolving many vague conclusions of classical geometry (enigmas) that the ancient Greek mathematicians left us with, and not only they but also the so-called geometrical wisdom of ancient Egypt because it was (and still is) vague, as well. It is a much older wisdom and not of human origin regardless of how hard we resist such afterthoughts and contravene them – they simply demonstrate themselves day in and day out, while natural science is merely discovering them bit-by-bit but not producing them as certain scholars would have us believe, since the substance and its regularities are already woven into the entire system of nature. Therefore natural science is a “researcher” and in most cases it is the individual, as centuries of written history confirm, someone who “dedicates” himself to the thorny path he has chosen, or a liaison between mankind and unknown wisdom. It seems that this could be the 12/24 background that is a link between the old and the new, which we will try to geometrically “clarify” in several ways through enigmatic themes, either of circumference or squaring the circle and more. Therefore, let’s repeat (for many of you) the concept of 12 only with a compass step by step because by knowing that we are prepared, and being well prepared is “half of the job. Use of shortcuts (linear division of the background) will deprive us of results.

The procedure is easy. Divide the radius of a circle with circle of the same radius. This is a division of the circle into 6 parts. The divisional or bisector circles create the intersections of their radiuses and such a radius is tantamount from its vertex pole to the other poles of the hexagonal circle. Thus we enter that range into the compass (therefore in shortened form we say radius 3).

With said range we divide the circle towards the perimeter of the divisional circles and thereby acquire new intersections that divide the (hexagonal) circle toward the perimeters of the divisional circles from opposite poles in half (we say radius 4).

From the 6 poles of the base circle, we divide the hexagonal circles with that radius in the direction of the perimeter of the divisional circles. Six new poles emerge on the arc of the base circle and we enter the same range into the compass, then we repeat the division from these poles.

The radius of 4 from the poles of the base circle “converge” with the semicircles from the 12 poles of the base circle. Now we enter the radius of the base circle into the compass and draw full circles from the 6 poles that came forth.

Again we enter radius 3 into the compass range and repeat same procedure from the 6 new poles of the base circle.

Hence we acquired, only by using the compass, the division of the base circle into 12 parts and sequences of intersections inside and outside of the base circle, the ideal specific “geodesic background” that brings forth successions of possibilities, and we could name it a specific “enigma background”. What you just learned (which I hope you have) has never before been publicly depicted in the history of civilization.

The circle’s circumscribed square (created by the intersections – only one of them).

Division of straight line bisectors into 12 parts.

Intersections outside of the circle enable the division of the circle (and system) into 24 parts.

One radius that comes forth from the duplicated creation of radius “three” and “six” from 12 poles of the base circle. What from or what is that radius of intersections 3 and 6 of the twelve poles of the base circle?

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The third star-shaped seven-sided polygon. Its radius divides the base circle into seven parts from the vertex pole of the base circle.

From 4 opposite poles divided into 28 parts (that will be used in another analysis) but right now we will use its circle and the division of straight line bisectors into 24 parts.

The circle’s circumscribed square of magnitude 3 diameters and one seventh diameter divided by 4.

Rectangle of circle area = square diameter divided by 14 times 11 square of radius times integer 3 and one seventh (equalization of two opposite rectangles constitutes the circle’s square area).

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This manner of construction of the circumscribed perimeter, i.e. of its square and rectangle and circle area is supported by another manner i.e. system of dividing into 24 parts, the construction of a circle’s inclosed square and the circumference of its circle with the circle of the system of the nine-sided polygon. In all of this, as I’ve been constantly stressing, it is important to draw the background as precisely as possible (in order to acquire the precise intersections and their radiuses). I wish to point out to all of you who are not “masters of the compass) that this should not be considered a big problem since the important aim is to understand the principle since in this geometry it is its essence, because it is universal, meaning without measures. Measures are more or less used concretely in our human spheres and activities, whereas universal principles deal with the relations between magnitudes and they particularly come forth from the relations of integers. Therefore this geometry is without marks or signs and is carried out only with a compass and an unmarked straightedge, limitless, a principle free of all measures, and in order to bring it closer to us it must be taught step by step, and in order to know how we have to create, as the geodetic would say, “a specific geodisical background”. That is why artifacts are bleak witnesses of all this, like a kind of final construction draft without a background hence the less skilled contractors often make mistakes, and that lack of knowledge actually results from being unfamiliar with the background. It would be ideal if the “builder” was both in a single person. But, let’s now see the second manner of constructing the scope and area of the circle only with a compass and unmarked straightedge, step by step.

The volume of the circle of the square circumference of the circle (read: quadrangle) is the magnitude of a side of a fourth of diameter 3 and a seventh of the circle’s diameter.

If we put in a large-scale circle square and a circumference square, we then have two rectangles with the area of the circle, and with their equalization we get the circle square.

The radius of the circumscribed circle of the two rectangles divides the base circle into 9 parts from the vertex pole (nine-sided star polygon, two “wings” hold up the side, hence polygon nine of 4 opposite poles along the sides of the large-scale rectangle circle would create 2 rectangle areas and square of circumference circle), is one of the possibilities that this background offers.

But here we also have a heptagon since the large-scale circle area’s radius divides the nonagon arc into 7 parts. Its two “wings” are points on the rectangle (its top sides) and the heptagon on the opposite pole of the bottom sides, and in tandem with the descriptive square of the circumscribed circle from the 4 poles of the two rectangles then make their equalization easy.

And this is a simplified seven from the 4 poles of the nonagon circle pf the first intersection outside of the circle of the star nonagon. All of this emerges from the background, hence seven and its relations on it.

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Such combinations come forth from the system of a “specific geometrical background” and in more than one way confirm the result in twofold or manifold ways, and never as single or autonomous and yet all constructed only with a compass and unmarked straightedge. A full analysis of the system would indeed be huge but worth the effort because it would give answers to sequences of other topics which perhaps even exceed the borders of our mind, though we conceive of them as legends described in ancient Egyptian writings, but since I exercise caution in these matters I prefer not to go into the subject because it could lead us towards the paths of mysticism that are full of unforeseen traps, and even though these paths are more attractive they are also more dangerous. So, stay away! That is precisely why the old Masonic skull and cross-bones symbol emerged, the ancient sign of danger and warning. Accordingly, the Masons or Templar Knights, the Free Masons, knew this because they experienced it. Let’s never forget that “Everything is in its own time”. In conclusion to this chapter on the perimeter and area of the circle, where number nine i.e. where the division of the circle is a nonagon, it is then easy to say that it is a trisection code that is but a somewhat simpler concept, which was already published in the “geometry for kids”, so by the way and for the purpose of refreshing the memory you can repeat it. And in continuation it would be good to analyze the radii of all the intersections on the base circle and the angle magnitudes jointly outside and inside the (base) circle, which would maybe reveal much more than we have presently anticipated.

Here it can best be observed from seven and discover how 8 divisions from 4 opposite poles of the dodecagon partition, and the third star heptagon polygon “forms” the circumference square of the circle and 8 divides the square of the circle area and the radius of the circumference square of the circle creates rectangular areas (shortened from 4 poles of the nonagon circle).

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If we were to further analyze in the same way that we established how both systems based on this “specifically geometrical background” belong to number seven and its lineage (times 4) we would come upon data that would tell us about a an ancient theme: about the orderly pyramidal objects with sides whose gradient is 360° ÷ 7 and ratio of height and base 1.66666′ or numeral ratio 5 and 3 (as noted in Egyptian hieroglyphic writings) and the (geometrical) basis of construction are the two mentioned systems of sevenths, each in its own way, and that is why I would choose to repeat it with the said background. But regardless of these by the way deviations, the essence of all this is a geometrical solution to the “vagueness” from times long past of a mathematical-geometrical nature that geometrically solves the problem entirely with a compass and unmarked straightedge, and this only because geometry has “taken” some other direction instead of the path that is right, universal and simple. I just don’t understand how these highly educated mathematicians can allow this “whatever comes to mind” attitude? It isn’t so much their “equilibrating” that irritates, but the “maltreatment” of kids with their “variability on a theme”, and therefore seldom can a kid learn to like geometry. To put it mildly, it is pitiful that we can find this in the textbooks for elementary schools, full of geometrical exhibitionism.

In this system of 28 divisions of the third star-shaped polygon from the four triangular bases of 12-sided circles a “lowering” of pyramidal sides occurs 4 times on the circle square area level with a pentagon construction. Here we show only one side and one pentagon.

The other system does not need to be lowered because its construction base is synchronized with the construction in which the circumscribed circle of the perimeter square divides the circumscribed circle of the nonagon into 28 parts, thus creating from the four poles of the nonagon circle a square around the center that forms the top view and front view system of a pyramidal object (only one side presented in color).

This is the same, but only demonstrates the whole division in sevenths from the four poles of the nonagon circle.

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You will notice that (upon reconstruction of division 28 of the third star seven-sided polygon with the addition of the pentagon) the lowering of the pyramidal side is on the six-sided line and not nine-sided, i.e. on the concept of the square of the circle area the square of which the base is of greater magnitude, and taking into account number Pi and number 3, the concept is solved in the manner of a midpoint “sagging” of the side that can be seen (a research air probe) on the Great Pyramid in El Giza. While all of this is incidental, in other words, not our goal because we are involved in how to construct the area of a circle only with an unmarked straightedge and compass, I cannot help expressing my strong feeling that there is another room above the now well-known central hall of the Great Pyramid and it contains the papers that would clarify the pyramidal secret and it is situated on the level of four-fifths below the peak. But, time will tell whether or not this is so. But let it be, as you have noticed I sometimes “go astray” from my planned geometrical path, although the pyramid in Giza is also an artifact that could provide us with sequences of answers that would put an end to the stories and hollow chimera but be a witness of its creator. However, nowadays the “creator” has become a tourist attraction (not only in this case, but wherever we look), because the “regulators” have become merchants, and this will last until the “creator” will one day “blow his top”, as the expression goes in our “modern” times. But hasn’t this been predicted a long time ago? Be it as it may, we will continue our analysis of the “background”, step by step, firstly with the radii of intersections outside the circle, only with a compass and unmarked straightedge (in our next chapter).

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CROATIA – RIJEKA May 03, 2014 Author: T. Periša

Web : Slim

English: S.F. Drenovac

omg! 🙂

I sent an important mail to Mr Tomo plz do help him read it and me so he can read it. thanks Slim