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Twelve

A NOTE AHEAD OF THIS CHAPTER

I never thought it would come to this, and it never would have, had I not been struck by reproaches from my own family because of all this, namely, wasting time and money in vain. Therefore, in order “to cool the tempers” and continue to do my work I first of all wonder whether there is anybody in this world who comprehends the value of this work and is sufficiently wealthy to support it financially? In this connection I have in mind an individual or the like, free from administrative forms, because were I to request this from my homeland, it would take so much time that one could write ten books in the meantime, and anyway I would not want anything from the homeland because everything here is in a disorder and superficial and regional, whereas I am a person who thinks globally, although somewhat extremist, since my life’s goal it to publish as much as I have learned from this geometry, as well as to publish more that 250,000 lines of verse that I have written, along with arrays of ideas. And that is all that I have to offer, and in return I only ask for a share from the person who would respond in accordance with the ancient law of King David: “May the share be the same for the warrior in the battle as for the man who tends the horses”. If such a person comes into view, he can contact me by e-mail. However, regardless of this I will continue my work as much as my possibilities allow. Thank you, and don’t begrudge me for this..

RI – RIJEKA, 31 December, 2011
Tomo Periša

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CHAPTER 9

TWELVE

Throughout the whole history of mankind, moreover throughout the entire existence of planet Earth along with the universe itself including the star constellations, number 12 somehow “wriggles” its way repeating its cycles so that we can from our human viewpoint align it within the temporal order of time with a strong impact on space, although it is also in a relative manner “naturally offered” to us for observation. I do not know whether these constructions of ours will give us more insight into number 12 but at least this spherical manner of geometry, only with a compass, will make some headway such as dividing the arc of a circle by way of the construction of number 12, various products which as “side effects” emerge if we apply the laws of Sacred Geometry (at least a half-way approach) of which one as we know is drawing (if nothing else) with semicircles or whenever possible with full circles if we want to comprehend the meaning of “products” or “side effects” at all, or the radii of various intersections and once again on the basic or initial circle. Number 12 could also be called the duplicating number of dividing the arc of the basic circle. Surely the division of the arc of a circle would be simpler if we applied rectilinear drawing (straightedge without markings – see First Book, Chapter “A” for Kids), but this spherical way of ours is somewhat different but it brings forth more “products”, and anyway since nothing in nature is rectilinear, we will first follow the path of number 12’s “coming into being” and its products, to thereafter interpret more about number 12 and the products that emerged from the spherical construction of 12, only with a compass, and that knowledge will certainly be useful somewhere.

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The circle of any radius (undefined) divided with its divisional circles of same radius and the intersections of the divisional circles circumscribed with their circles of same radius.

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We aforesaid that this radius “forms” the six-sided star polygon drawn from the peak pole and subtended pole of the basic circle.

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Let’s disregard the same division of divisional circles but we see that this division forms its own intersections (outside of the first circle) hence we circumscribe them with a circle of their radius.

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That radius of the six-sided poles of the basic circle  divides it into six more parts – hence, twelve parts.  

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Then if we depict the same radius and acquire from those six poles a constellation that we will “ponder” (we depicted with semicircles and they connect to the circumferences of the divisional circles of the basic circle.

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Now let’s only observe the intersections.

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This radius divides the basic circle (starting the division from the peak pole of the basic circle) into ten parts. We “filled in” only two of the 12 poles of the basic circle (from other poles, which means, duplicating the 10 series).

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Within the circle, serialized sets of intersections form, among which are the ten internal series (we only employ the arc of the basic circle).

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The interior intersections closer to the arc of the basic circle  divide the arc of the basic circle into 8 parts.

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If we now take combined intersections within the circle (meaning radius 12 and divide the circle into 6 parts) its radius divides the circle into 12 parts (the internal confirms the external).

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Again the external first (the divisional external twelve) divides the circle into 9 parts (3 poles of 12 filled in), thus series of 18, 36, and so on, are possible.

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What about the touching points on the perimeters of the divisional circles? That radius divides the basic circle into 12 parts but it “forms” the first spherical twelve-sided star polygon.

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Once again we take the combination – intersections of radius 12 and star-shaped polygon 2 x 6 – starting the division from the peak pole of the basic circle.

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That radius divides the basic circle into 36 parts (we „filled in“ all the poles of the basic circle). 

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And now, one more product with the same combination in line with the arc of the basic circle but outside of it.  

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That radius divides the basic circle into 24 parts (all the poles – all 12 are filled in thru division).

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Let’s go back to radius 12 and verify the correctness of division by a so-called “rough estimate” (ancient Egyptian system of verification and divisions solely from the peak poles – two subtended – „as above, so below” – an old Egyptian proverb).

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We divide the circle with its radius into 6 parts.

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Only then do we notice the internal intersections in line with the arc of the basic circle.

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The radius of the intersection divides the basic circle into 36 parts. Surely we did not analyze the other series of intersections of this constellation, but just some of them, we could say, thos that are essential.

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AFTERWORD

Upon observation of the order of creation of constellation twelve, one gets a strong impression that the reasoning of the ancient philosophers was right (read scientists or scholars of nature in comparison with present-day philosophers who are not philosophers – I assert – but “storytellers”) and they came upon the idea of space and time as absolutes (inthis case I make no mention of energy, the third absolute). Hence, prior to any undertaking there was infinity (read indefinity) thus space in the same such time (of course energy, too). But the moment we circumscribed (in our case with a circle) we defined a space (with a defined quantity of something. But time also had to be defined, and all this was initiated with the process or processes of division. There is no doubt that this self-observation was purely mental, yet I once more aside with the ancient thinkers-philosophers, in the real sense of the word cast off a long time ago, “builders” – because humankind is prone to easily forget its builders (its foundations), which could not be identified with wisdom because the wise never cast away everything, but take what is good and cast off what is wrong or rectify it until they achieve the building that they envisaged, whereas the unreasonable persons demolish everything and build over and over again endlessly. To them the wisdom in the story of Sisyphus was in vain.
Well, geometrically we have observed the links of number 12 with 9, 10, 8 – number 7 was left untouched this time. Had we done that we would surely have completed the entire system of numbers, namely divided the arc of angular minutes, regular polygons, because this way enables us to construct regular polygons and prime numbers and complex numbers and their products, once more only with a compass, namely spherically just the way that it is defined in nature.(step by step).

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