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The Last Star (In the sign of number 9)


(In the sign of number 9)

As usually happens in our human life, Man can never really know what the next moment or next day will bring, or perhaps such cognitions are exclusively the privilege of those “volunteers” who are led by the invisible hand of the spirit (a dimension we honestly know nothing about); those who relinquish themselves to such a road. Indeed, I truly had the intention (strictly due to human and financial reasons) to bid farewell to all you readers of these pages, but on second thought when I think of how I have already squandered some 60 thousand dollars, then I can risk a few more and may it be as God wills! In the long run, I am His “volunteer”. Certainly, after all that has been implemented, it’s far from simple to get back into a “normal” manner of living, especially because I have gone too far for such a comeback, particularly since I’m aware of how much new and unexampled truths can still enlighten our world through the use of the internet, in particular for loners like me who are outside of institutions and as such without any kind of support (in so saying, I don’t have in mind the moral support that I get from people from all parts of the world through e-mail messages and comments, regardless of their political or religious affiliations). Thus, this “last star” also has a lot to say in this chapter as well as in the next one that refers to the equilateral pyramid. Therefore many will be happy and their gladness is to some extent my consolation, particularly when such message arrive from ancient regions such as Persia where people still greet one another with a “God bless you”.

Hence, in this chapter we are talking about something that here in the west, since Archimedes to this day, is considered impossible: division of the circular arc into nine, that is 18 parts only with a compass and straightedge, and conclusively with number 3 and its close relationship with number 5. Therefore, let’s analyze step by step a segment of the “last star”.

* * *


The radius of a circle is divided by semicircles into the 6 parts of a “flower pattern”. Every other pole rectilinear – hexagonal star polygon and every other semicircular – rounded star polygon and straight lines of diametrical poles to rectilinear intersections and rounded star depicted circle.

* * *


Thereafter with same radius this circle is divided from the peak pole into 6 parts by full circles, and they themselves. That’s the background of our analysis.

* * *


And one more background element. Every other intersection of the divisible circles is rectilinearly increased with lengths, which then intersect the basic circle. From the peak pole of the basic circle we now analyze these intersections with a compass. The second pole from the peak pole (from center we inscribe full circle of that radius).

* * *


That radius divides the basic circle into 9 parts (from the opposite pole it would be 18 parts)

* * *


Let’s go back to the first intersections to the peak pole with the compass (we also show theses radiuses from the center).

* * *


That radius divides the arc of the basic circle into 18 parts – an octadecagon.

* * *


The third radius intersection conforms to intersections of the circles with which we divided the inner circle.

* * *


That radius divides the arc of the basic circle into 9 parts from the peak pole.

* * *


The fourth intersection …

* * *


… divides the basic circle into 18 parts.

* * *


The fifth intersection

* * *


Radius divides basic circle into 18 parts …

* * *


… and 6 intersections

* * *


…divide the basic circle into 9 parts (the depicted rounded nonagon). Thus we have attained the sequences of the nonagon and octadecagon of 6 radiuses.

* * *


Therefore, the equilateral division of the circle into 9 parts of peak angles in the 40° center.

* * *


If we connect peak pole with its diametric first intersections we have attained the peak pole of a 20° angle and division of a circle into 18 parts.

* * *


If we link basic circles with their lengths (every other) and the star hexagon with the first radius analysis and its peak pole and from there the circle’s depicted base,

* * *


… the base divides that circle into 4 parts …

* * *2219

… and if we proceed in same way with the other radius and inscribe a circle from that peak …

* * *2220

… the radius (its magnitude in the compass) divides that circle into 5 parts.

* * * *


We will break off here and go further on in our next chapter since I prefer not to encumber your minds with the weight of data (because many of my readers are secondary-school pupils) and this kind of geometry demands getting used to it. A long time ago I read a mythological book about Moses which of course was not biblical (canonical), by German author Edmond Flug, and the story says that when Moses stayed on Mount Sinai for 40 days to receive the Ten Commandments, he used that time to go to school with the angels. An interesting narrative, but right now I won’t go into that because we simply have to stick to our topic since the data or products of this step-by-step kind of geometry entirely with a compass and straightedge demands to be promulgated. It seems that the geometers or “measurers” of the ancient cultures of the “bountiful crescent” (from Egypt to Persia) did not reveal all their knowledge to the Greek mathematicians but only partially and they too were not given bestowed with a complete knowledge, most probably to prevent their going “astray!”. Are we now making an accession to “complete knowledge”, I know not, and prefer not to burden myself nor you with that question. As the folk proverb says, it will be revealed: “In the course of time”.

RIJEKA – CROATIA, May 23, 2013
Author: T. PERIŠA

One Response to “The Last Star (In the sign of number 9)”

  1. Ricardo says:

    “God bless you” for the good news.

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