## Pythagorean Theorem – Verification and Effect

SPECIAL CHAPTER 3

**„PYTHAGOREAN THEOREM“**

**(VERIFICATION AND EFFECT)**

Since the present time is a time of global disorder among interpersonal relations and relations between man and nature, it is clear to me that I should not anticipate that many will make an effort to correct things that have been erroneously conveyed since ancient times, hence mistakenly comprehended. Who cares nowadays about an “illogical” fragment of a natural science (geometry), when geometrical tales and theories are much more attractive regardless of how meaningless (dissonant) they may be, because these are “modern times”! The more anything is intricate, it is that much more interesting and this does not apply only to our theme. Let’s look around us. A painter daubs a canvas with his brush and asks “see that?” The observer, of course, to avoid being considered an ignoramus, replies “I sure do!” A poet jots down three words from his stream of thought and asks “do you get the meaning?”, and the reply is “I get the picture”. These are just some commonplace examples of the state of our civilization (purportedly progressive), with its heritage of concealment, “conclusively said” with the objective to “subjugate” the masses, for what would happen if a simplicity that everyone could understand was revealed? It would generate a state that is called equivalence! Then what kind of a world would that be? It would be a world that never was. Then who would be the “boss”?

It seems that we have never learned anything from history. And because of that “nothing new” buzzword, the downfall of civilizations has taken place, one after another, and this civilization of ours (I conclude) unfortunately won’t be exempted.

Personally I prefer to go to “the other side” for once, indeed rather than to accept a “delusion”; and so with a clear conscience I wish to underscore that concealed knowledge was something I never concealed, and whatever knowledge has been imparted to me I have always conveyed it to the world, not to make life easier for myself but on the contrary, knowing it would make life more difficult because I will grasp the perceptivity that we(man)is not the above all in time, space, universe.

So, let’s go further on with the regularities of the so-called “Pythagorean theorem”, and start out with measurements to make it more clear-cut for our grade-school students (the first part of this chapter), and thereafter deal with the product (the second part), somewhat more complex or, as mentioned, the “impossible” part.

Symmetrical line construction of straight lines (right-angled) on lengths (measured or random). The symmetrical lines divides it into two parts, …

… and then into four. Transfer three parts onto the vertical line (the other leg). The right-angled triangle proportion of the legs is 3:4.

It is apparent how the symmetrical lines of division are helpful.

To acquire the same division of the hypotenuse, the right-angled ratio of the sides is 3:4:5.

With compass only, we construct the squares of the sides (legs) and of the hypotenuse.

Here, once again we have the help of the lines of symmetrical division of the legs in constructing the square of the hypotenuse.

And then, for division with the compass…

… so that we can boil down any randomly given length, only with a compass and unmarked straightedge, to the ratio of 3:4:5 …

… and divide them into squares of same surface area 9:16:25

* * * *

And this 3:4:5 ratio is the only one that matches with the “Pythagorean theorem” – The sum of the squares of the length of the legs is equal to the sum of the square of the hypotenuse. The same that can be said about this ratio is that it has a regularity of expansion. The first 3 always expands further by 3. The second 4 always expands by 4, and the third 5 of the hypotenuse always expands by 5. Thus the sequence that follows is 6:8:10 parts and thereafter 9:12:15 (example 9×9=81; 12×12=144. Sum = 225 and the square root of 225 = 15) etc. The transfer of parts is simple even though it is presented only with semicircles, and we know that in sacred, ancient, divine geometry everything is constructed with full circles and full straight lines along with the assistance of acquired intersections since all together they create always newer and newer products, and all this is constructed only by means of a compass and unmarked straightedge (a universal code) and if measurements are added on the same outline, then we get a concrete case of a material nature (such as the ancient buildings. However, we are interested in what else the “Pythagorean theorem” reveals. I still call it by his name, even though it is obvious that Pythagoras simply documented knowledge that he happened to come across (albeit that the ancient Egyptians were also doing the same), but we can still only bode as to who was the actual creator of that knowledge – so let’s just call him “creator of knowledge”. But let’s continue, step by step, to “ascertain” ourselves, thus we will now employ measureable values for the sake of clarification. Hence, let’s introduce into our outline the magnitudes of current measurements 6cm and 8cm and 10cm (which enables my working on paper format A4). So, 6×6=36cm2+8×8=64cm2 and sum 100cm2 (square of hypotenuse), but our interest is in something else: the described circle of such a right-angled triangle.

So, in accord with the outline of the constructed triangle, its center is on the hypotenuse.

The described circle or circle of the hypotenuse diameter.

With the help of properly constructed squares of the hypotenuse we get a division of the circle into four parts, so let’s use this (semicircles from four poles of the circle).

With straight lines we “legalize” this division.

Extend hypotenuse 3 and its opposite side.

We got a square the size of leg 4. What does this tell us?

The described square of the circle’s disunited proportion with the voluminous square.

Square of the circle’s surface area. What does it tell us?

* * * *

It tells us something amazing. Whoever kept abreast of the chapters of this geometry knows that I simplified the Pi number and employed it on the circumference of a circle, or 3 whole diameters respectively + one-seventh of a diameter = circumference of a circle. Concrete example: diameter = 10 cm. Next: 1017 = 1.4285715 cm + 3 diameters (30cm) = 31.4285715 cm length of circumference, thereafter divided by 4 = 7.857142 cm = square of the length side of circumference. And we simplified the surface area of the circle, if you recall (the same applies to the Pi number, but on the opposite side: 4 diameters, and 4 diameters divided by 14 times 11 (number Pi times PiT = 4). Four, of what? Four diameters and the 4 diameters is the constructed square of the circle. It helps us construct the right-angled area that is the square of the diameter divided by 14 parts times 11 parts (see chapter Education for Children: the Second geometrical enigma) and equalize the right-angle through the procedure of verticality in order to acquire the square of the surface area of the circle with geometrical deftness. But the most important is the simplicity of construction of the circumference with the help of the right-angled triangle of the ones pertaining to the legs, and that would be the message or key to go further onward, towards new cognitions by means of this relationship conveyed through symbols or simply put by means of the artifacts of ancient civilizations. Not only them, but also by means of the mysterious buildings whose purpose remain unknown to us. All this might be revealed by means of this right-angled triangle that corresponds to examining the “Pythagorean theorem” to perhaps discover the message of all this. However, one thing is certain, tjis relationship not only simplifies finding the solution of the problem of circumference and other geometrical enigmas but also solves the third geometrical enigma in a simple and pure geometrical manner – evidently. As regards the angular analyzing of such a right-angled triangle or triangle of the “Pythagorean theorem”, it at least solves the issue of who built the pyramids by a relationship of angles, although I do not wish to speculate about their purpose. Instead, I only follow the number that “speaks” about their builders.

Hence, I am determined to proceed in detail (to the extent that they are given to me), step by step, or as one would say in present-day popular jargon, “with forensic patience”. I only regret that my generation and many other generations were mislead by the knowledgeable. Even to this very day, the “Pythagorean theorem”, unrealistic as it is, still remains in force. Nobody even suspects how important the real Pythagorean Theorem is in physics for elimination of that energetically reckoned “impossible”.

RIJEKA – CROATIA October 03, 2013

AUTHOR: T. PERISHA

WEBMASTER: SLIM

ENGlISH: S.F. DRENOVAC

Add the fact that; 3 cube + 4 cube + 5 cube = double Cube of 6, and also that inside the circle the 3-4-5 triangle is part of a 24 side poligon,so, ( break cirle into 24 parts and choose a start point, draw line of 5 spaces to one side and draw line of 7 spaces to the other side ( ratio7:5; because you can draw STAR shape of 7 spaces and 5 spaces on a 24 partition), and the diameter of that cirle will be the hypotenuse of a 3-4-5 triangle. STAR SHAPES are very usefull !!! If you make the 7:5 STAR shapes togheter on a 24 partitioned circle youll get the picture. If you draw also the STAR of 10 side polygon; and do STAR shapes inside STAR shapes; you get 3 dimensional perspectives, very neat. Thanks again Mr Tomo.

correction – not double cube of 6 – JUST CUBE OF 6 🙂