free hit counters

Nonagon and the Egyptian Nine

CHAPTER 6 (4TH Book)



Since the present-day spirit is, regrettably, far behind the spirit of ancient simplicity we still find in the texts of our worldwide and well-known encyclopedias (one of which is Larousse) that hold fast to the opinion that “the construction of regular polygons only with a compass and unmarked straightedge is impossible”. What is the cause of this? We would say, the degree of Europe’s state of mind, which is apparent from the general conditions of life and its human (or better to say inhuman) levels. Everyday life speaks for itself. The striving for something better is certainly present, but our cultural legacy is still a wall without a door. Plainly said, instead of technological progress bringing wellbeing to everybody or at least to the majority, it only benefits individuals or the minority. Hence, such an autonomous mindset cannot or will not accept simplicity, not even the easiness of this geometry. Therefore it’s no wonder why it is difficult to comprehend this kind of geometry only with a compass and unmarked straightedge, for which I’m absolutely sure that so far nobody has ever drawn it in this way since its plainness of construction appears complicated, especially because it is unmarked (thereof its step-by-step presentation). Moreover because of the oftentimes repeated technological “not exactly” comment, since one of three parts is 20.03° and the second is 20°, whilst the third is 20.12°“. Why didn’t these “supervisors” read these pages more cautiously so as to have them fall into place in their “intellectual” consciousness, because this geometry is a universal scheme of construction that illustrates how or in what way they are performed (regardless of which measurements are used) and actually the only problem is in the “primitiveness” of the tools of of the draftsman who uses them. Here’s an example: Most probably nobody will ever be able to divide a simple circle with its radius into 6 parts and that each part will be a hundred percent exactly 60°, which is logical and not so important. The reason lies in the puncture needle of the compass or offset of the pencil or the straightedge. One day that will be possible when projecting will be performed with an “electronic compass”. But until then, we have a long wait and this will be achieved by some future generation and therefore I say that for the time being it is not so important, rather what is important is how, and that would be by means of “visual communication”. As for the good question of how was it possible that “ancient people” knew? I believe that it was because they were closer to the spirit of nature (in this chapter this will be confirmed by the tri-star system in the hieroglyphs in which we will notice a tight connection between 3 and 5, in other words better to say between the square of number 3 and prime number 5, where the geometrician of those times would just shake his head if he saw our present-day mathematics in the same way as I pity the elementary-school children of today who no longer draw, and their numerical “exhibitions” do not contribute to a crystallization of the mind and its development but instead cause a chaos of irrelevant information creating thus a creature that is lsing some of its natural senses, as I’ve illustrated in the last chapter. Anyway, since many of you have requested, I will repeat the nonagon in a less complicated way, with the addition of an Egyptian mode or a pyramidal draft in which 360 sevenths (2 times) are the pyramidal slopes “naturally” emerging from number 5 and in the first case we will proceed step by step with the first inner (inside the circle) radius of number nine resulting from the hexagonal circle, respectively from its number three or its star polygon (truncated or with semi-circles) and only with the compass and unmarked straightedge. Perhaps it is high time for certain “impossibilities” to be removed from the encyclopedias or will we have to wait for a civilization with another consciousness.

* * *40601

A circle of a random radius divided by circles of same radius into six parts (always keep an eye on the basic circle since most of the changes happen there).

* * *40602

Within the basic circle we have by such division acquired a so-called floral pattern, and on the circle itself the points of divisible poles (first intersections of divisible circles.

* * *40603

Lengths divide the circle (with straight lines all the way to the perimeter that form the divisible circles), which once again mutually intersect. Depict a circle around the intersections of that radius.

* * *40604

The new and larger radius of the poles of the basic circle passes through every second pole and produces a pattern within the pole – a rounded hexagonal star-shaped regular polygon (drawn semi-circles of the referred to larger radius all the way to the perimeter of the divisible circles).

* * *40605

The rounded star polygon inside the basic circle has its intersections. Depict with a circle of same radius.

* * *40606

With a straight length (one for the time being) connect every other second pole on that circle. The lengths dividing the first or basic circle (two lengths) will help us.

* * *40607

The third length of division falls vertically onto that length and divides it into two parts. Therefore we take into the compass range half of that length as the radius of one smaller circle (presented by semi-circles).

* * *40608

The radius of that circle is even smaller than that of the circle of intersections of the star polygon (we depict it from the center). Everything that we have so far described remains drawn. – we follow the further development.

* * *40609

The radius of the circle divides the arc of the first – central circle into 9 equal parts from the vertex of the pole (from the opposite – free 18, from the division of circle into 4 parts it would be 36, etc. in all regular polygons). Now who dares say that it is impossible!

* * *40610

However, as we have previously noticed in some earlier chapters full of drawings of divisible circles, every regular polygon produces intersections from its poles whose radius divides the basic hexagonal circle into its duplicity (hence its exterior nonagon circle . . .

* * *40611

. . . divides the basic hexagonal circle into 18 parts (division usually starts with said radius from the vertex pole, part by part, until it ends up again in the vertex pole). This means, if we were to convert the acquired poles into triangles, the vertex pole would be 20°.

* * *40612

Interior intersections. Constellation of nonagon circle out of 9 intersections of the basic circle.

* * *40613

Eighteen-sided polygon.

* * *40614

Well, a bit of analyzing won’t hurt. Into how many parts does the nonagon radius divide the star-shaped hexagonal polygon?

* * *40615

Lo! It divides it into 7 parts (if through the poles of the division from the center we get a proper division into 7 parts of all the circles that have this common center). Who can still assert that the division into 7 equal parts only with a compass and unmarked straightedge is impossible?

* * * *


What more can one say? I would write and draw extensively because arising from this not only does sequence upon sequence emerge and not only of regular polygons but sequences of regular constructions (as I announced in the last chapter), so I will now roughly announce a somewhat more detailed analysis of Egyptian 9 that stems from the first exterior radius of number 5 on the basic hexagonal circle, the radius of the three poles of that same circle (in the chapter on construction of number 5 only with a compass, and in order to avoid repetition you will come up with the pentagon circle thanks to the fact that I will just draw the surface and point to where number 9 can be found). Why am I truncating it like this? The reason is because number 5 has not been declared an impossible construction. Somebody had found a way (I learned this in school), even though it brings about nothing else but a pentagon. However as you have seen for yourselves, this method of mine brings about sequences and sequences of results – however I really cannot go into extensively writing about this because that would cost me dearly due to a succession of circumstances (the cost of supporting everyday family life, friends who are unable to return what they borrowed from me and numerous other unforeseen situations). Once one of my readers asked whether the government administration has ever verified my opinions or conclusions. Oh, give me a break! The administration lives on such a debt that future generations will suffer to return it. If only I were younger, but here I am almost 64! Otherwise I’d go away into the world and I’m sure that somewhere my opinions would be verified – these and many others that cannot be realized here. As folks say, the situation here is “enough to make the angels weep!” Yet I still manage to bear it, therefore please pay no attention to my grieving but rather focus your mind and perspective on the geometrical because it will by means of genetic heritage remain in you, and even more important, in your children, hence in the future generations. Therefore, the Egyptian 9, its genesis from the three pentagon circles of its constellation. (But for the sake of joking a little: From the constellation of the three stars of Sirius).

P.S. In reference to my going away or the desire to go about lecturing on the subject of this geometry, unfortunately the only foreign language I know is German, and I only have an understanding of English. Hence, these translations by my 80-years old friend, S.F. Drenovac (just in case such an idea to engage me enters your mind).

* * *40616

So, the system of division of the circle into 12 parts by bisectors of the hexagon.

* * *40617

Radius 3 from 12 poles. The first exterior intersections. The pentagon. Bisectors are not even necessary save for a one and only (to divide the circle in half). Why the 12 basic circles from the 12 poles, is to be explained in a subsequent chapter.

* * *40618

Pentagon circles of three triangles from the pole of the basic circle (HU-MAN constellation)

* * *40619

We described their intersections with a circle, which is its radius (seven is hidden – for a second time).

* * *40620

Its radius divides the basic, first hexagonal circle into 9 parts. A nonagon.

* * * *


We will stop here even though this is just the beginning. We got what we wanted – the nonagon. Two separate cases. By the way, 5 and 7 are as much as necessary (for this chapter). The latter is only one constellation of 3 pentagon circles (and there are more) with the goal of a number nine outside of the hexagon circle, and the reason for this is simple. The tetragon number nine is the square of the squaring of the hexagon or basic circle. The “pyramid-minded probably assume what comes next”. So, what’s next? Don’t blame me for my occasional bitterness. Next, I will let the Lord guide me, and in his honor and my gratitude I will drink a glass of “Noachian” consolation.

RIJEKA – CROATIA January 24, 2014
AUTHOR: Tomo Perisha
ENGLISH: S.F. Drenovac

2 Responses to “Nonagon and the Egyptian Nine”

  1. Ricardo says:

    THE AVERAGE of our needle points will Pi itself to our results, you really dont need the electronic compass that much, I believe.
    When we find an average of anything, it is the same as drawing a circle and finding Pi = average; of all results added and divided by the diameter of results added. (SUM/quantity of Sums ) So take in account the fact “your needle” is not that unprecise when you average it.
    The less points in our circle, the less precise; in logic terms, but the compass doesnt say that about numbers 3 4 5 6 7 8 9, now does it??? The centers of those needle points are important but precision is like a book, how precise can a book be explaining itself? Maybe a book of numbers, but even so…

    Cheers again.

  2. Poštovani!
    Gdje mogu nabaviti tj. kupiti ovu knjigu ‘Sveta geometfija’ Tome Periše?
    Moja adresa: S. Širca 64, Prekolakra 34550 Pakrac
    moj mob: 099 599 2438
    Unaprijed hvala.
    Lijep pozdrav.

Leave a Reply

Powered by WordPress | Designed by: suv | Thanks to trucks, infiniti suv and toyota suv