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Pythagoras – Seven

Chapter 9

So much has been said about number seven in the course of the centuries and all around the world that my overview on the subject would be redundant and there would not be enough elbow room to say everything. If anybody was to write a book about number seven, it seems to me that a human lifetime would be too short just to replicate everything that has bee said, and yet it would still be an enigma and the issue of precisely why number seven from a geometrical aspect is no longer an enigma, but in this chapter you will see for yourself that it is the only number whose lineage is not compatible with the Pythagorean theorem of the right triangle since it has no zero point, but invariably appears with an excess or deficit of surface area. Since we have already (relatively) found the modus of geometrical overlaying of areas of the right triangle, I won’t waste too many words and frankly speaking this will make life easier for me and my translator, and for all of you it will expand your power of cognition and perception. Once again I wish to repeat that this kind of geometry only with the use of the compass and unmarked straightedge (no letters or numbers) and step—by-step (drawing-by-drawing) manner develops the power of observation and can be conveyed into ones daily lifestyle, in other words into every segment of human activity because such activity rests on the decision-making approach. The result subsequently verbalizes the character of the performer or is his reflection. I know that some may say that perfection dows not exist. It could be (for the time being), but whether we admit it or not, all of us strive to achieve it and we must never forget that we are still trying to reach it, but more on this topic will be said in a brief “precaution” at the end of this chapter.

* * *040901

As usual, we will start with the hexagonal circle divided by circles of same radius, and sevenths from the vertex pole that divide it into seven parts.

* * *040902

Here we have the first right triangle of lineage seven. Angular size (slope of hypotenuse: 90° ÷ 7×3 = 38.571426° or 270 sevenths).

* * *040903

We convey square of base leg to area of square of hypotenuse.

* * *040904

The area remainder on the surface area of the vertical leg tells us of the excess of the sum of surface areas of the legs.

* * *040905

The radius of the circle of the hypotenuse divides the basic hexagonal circle into nine parts.

* * *040906

The same division of sevenths on the opposite pole of the hexagonal circle forms two right triangles (90 ÷ 7×1 = 12.857142° or 90 sevenths), thus (90 ÷ 7×5 = 64.28571 ÷ 4 = 450 sevenths)

* * *040907

This time we transfer the surface area of the vertical leg to the surface area of the hypotenuse and the remainder to the basic leg.

* * *040908

Once again we have an excess surface area on the sum of surface areas of the legs…

* * *040909

… whereas on the smallest right triangle of sevenths we get an excess surface area on the surface of the hypotenuse.

* * *040910

From the right pole of division of the circle into 4 parts, divided by seven we get two triangles (we only analyze the first one): (90 ÷ 7×2 = 25.714285 or 180 sevenths)

* * *040911

To surface area of square of the hypotenuse we transfer the square of the basic leg.

* * *040912

Remainder is transferred to square of the basic leg. The excess goes to the square of the hypotenuse.

* * *040913

The last division from the opposite (left) pole or full division of circle into 28 parts (4 times 7)
(90 ÷ 7×4 = 51.428571 or 360 sevenths of the whole)

* * *040914

Once again we transfer the square of the vertical leg to the square of the hypotenuse.

* * *040915

Thereafter part of the remainder is transferred to the square of the basic leg …

* * *040916

… and then the whole remainder. The excess goes to the surface area of the sum of the legs (quite obviously).

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The circles and relations on the basic circle have not been analyzed. You can do that yourself (apart from the very essential relations of seven and nine, and if you do that you will notice a small and interesting Golden Ratio or the ratio between numbers seven and six or the measuring magnitude of a palm in the “angelical” system of measures according to the prophetic scriptural book of prophet Ezekiel in the chapter about the New Jerusalem. But lest we get lost in numerical calculations for which I know would bring forth sequences of results and actual values such as measurements (spatial terrestrial and value measures of distances of planetary character and more), temporal (the seasons, cycles on the earthly and planetary levels) and many other things, we will nevertheless stick to the domain of pure geometry since we are analyzing the Pythagorean theorem of the right triangle in a specific manner. The system of measures for number eight still remains for us to analyze even though we have partially started it with the slope of the hypotenuse at 45° or (90 ÷ 8 x 4 = 45) or the beginning of analysis of Pythagoras Theorem, however since we have already come into contact with number nine we will for the moment skip ordinal number eight and its lineage. Instead we will analyze nine and its lineage, 90° divided by 9 or the angular slopes of the hypotenuse 10, 20, 30, 40, 50, 60, 70 and 80 degrees of the system of division of circles by 4 times 9 or the thirty-six sided polygon and its 6 or 7 or 8 values, respectively. We will implement the same way as with number seven using the familiar construction system from one of our earlier chapters of this geometric opus. This is why the pages that follow make an announcement of the next chapter and at the same time bring forth the possibilities of the thirty-six sided polygon construction for all those readers who are constantly looking for a thirty-six sided polygon on these pages, even though there are other ways, one of which is simple and arises (outside of the circle) from the concept of the hexagonal division of the circumscribed square of the divided circle. However, we will use the concept inside the circle.

* * *040917

The (internal) radius by way of division of basic circle’s radius of intersections with their circles into six – thw nonagon on the basic circle from 4 poles (diametrical) = 36-sided polygon (90÷9 = 10 x 1x2x3x4x5x6x7x8)

* * *040918

As regards the circumscribed circles (circles of the hypotenuse) the desirable division of these radiuses is on the basic hexagonal circle.

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Since as of lately I’ve been getting “mails” asking for “books” that are adverted to as such only by name, that is to say for the features on these web pages, I must frankly tell all of you (my known and unknown visitors to these pages) that there are no actual, printed, books – and even if there were, just imagine how much the postage charge would cost to send them from one end of the world to the other! Or just imagine how much the printing of such books would cost (four of them, not counting the Geometry for Kids) which have to be bilingual and in color! I once made such a calculation for my poetry, a per mille of which you can find on these web pages – without the English translation – (only a transcription by two young women, volunteer coeds of the Faculty of Philosophy, more or less to simply make sure of the grammar, because otherwise I do not allow anybody to change a single line of verse). It would cost me 150,000 dollars – for 13,000 poems – or 330,000 lines of verse written in the last 11 years, not counting what was written and printed before that (in a circulation of only 500 copies). So you can just imagine what the cost of geometry would amount to. Without a hundred thousand dollars I would not dare undertake such an enterprise. That is why I have given my approval to everyone (who asked me) to freely download the web pages and make scripts for themselves since we seem to be living in extraneous times. Here’s a typical illustration! It’s about me and an old friend of mine whom I’ve known for thirty years. I lent him a considerable amount of money (as mentioned in a few of my recent chapters, I sold a building site on the island on which I had expected to peacefully spend the late time of life. The children would go their own ways, and I would find enjoyment in the sun and sea, in a small boat aware of the dancing of the fish around my hook – something like Hemingway’s old man and the sea). My “friend”, upon discovering the loss of the money on the stock market, even feigned a report that he had after 2 months returned the debt (40,000 dollars – luckily this was just the advanced half!). But I’m not all that disconsolate because of the money. I’ll manage somehow, but I’m sorry because there are no more friendships – kinsmen – I’m not like Diogenes of Ancient Greece looking for a man, but it does seem as if history is repeating itself. For instance, here in this world around me we keep on hearing “Tesla is a Croat” (born in Croatia), but it’s not so “Tesla is a Serb” (the son of a Serbian Orthodox priest), but it’s not so, because he was an American! Other Nobelists of ours, like Dr. Prelog, awarded for chemistry was the friend of a dear friend of mine, Dr. Dolinar, world champion in table tennis in 1956, who was a close friend of actor Gregory Peck – yet everybody shouts he is ours, he is one of us! No, I claim that Dr. Prelog was Swiss! When somebody needs you, he doesn’t exist, but when such a person is gone everybody boasts that they knew him. So to speak, if I could find somebody to evaluate what I am doing, even if Chinese, and my work would contrive some award, I would say that I am a Chinaman – publicly! But, a cautionary note: do not regard this geometry as esoteric – prophecy, divination, astrology and the like. Don’t forget that. To get started, at one time someone “recommended” the advice of prophet Jeremiah regarding all of this and that’s the spirit that guides me, namely whoever knows even a little about the commandments given to Moses on Mount Sinai very well knows that the esoteric theories are “abominations” regardless of the profits they bring. I’m not saying that they are beyond discussion, but whoever knows the third enigma (which I intentionally avoid) will not fool around with it. Only the entity that “hits” you can heal you. All of you, both young and old, unknown friends (not of me, but of these pages) can help me by sending letters to the mathematical-geometrical universities of your countries and call attention to the need for my works evaluation and verification. Suspecting the outcome (confidentially) I’m keeping this last enigma, and it will be what will be. So, until the next chapters, greetings to you all!

CROATIA – RIJEKA February 22, 2014
AUTHOR: Tomo Perisha
English: S.F. Drenovac

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5 Responses to “Pythagoras – Seven”

  1. Ricardo says:

    Did you guys have a good Pi day??

  2. Ricardo says:

    now i got it….22 Feb – chapter called 7 – on Pi day =22/7 . hehehe awsome connection there.

  3. Ricardo says:

    I was playing arround and found this 3-4-5 triangle numbers:

    396 – 528 – 666

    smaller version is, 3.96cm – 5.285714cm – 6.666666cm

    aint this symbolic?

  4. Ricardo says:

    And this one is amazing too:


    – if you notice the sequence goes backwards 3,2,1 and then 4,3,2 and 5,4,3

    now draw it with measures as a 3-4-5 triangle.

    3,21cm 4,32cm and 5,43cm ;

    pretty cool!

  5. Ricardo says:

    Took me a while, but I think there´s alot to this exercise, at first I thought its just about areas…but…its not only that, its all about 1\4th of a circle, and all that you can do with 1 quarter. Since Pi is an average or a circular average, whats Phi??? a spiral average?? hehehe… Is MrTomo making a next chapter?? I wanna know where this leads…cheers to you all!!

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