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Podjela kocke (kub 7) – Broj π (Pi)

POGLAVLJE „E“ ZA DJECU

PODJELA KOCKE (KUB 7)

BROJ π (Pi)

KUB 7 (6 + 1)

Netko će se upitati čemu potreba za podjelama kocke na dijelove i zašto time mučiti djecu (dob od 10 do 20 godina) – drevna definicija do punoljetnosti – i to samo sa šestarom i ravnalom bez mjera, kada je to već ionako „razjašnjeno“ u geometriji, a i nije važno jer današnjim tehnološkim pomagalima možemo sve pa nije od neke bitne važnosti ako je i „približno“! To „približno“ možemo usporediti sa onim koji trči prema cilju i posustane ispred samoga cilja a onda kaže da je skoro stigao. Opet je s druge strane takav odnos znak nepoštovanja i nekulture prema onima koji su se trudili već 2500 godina ove naše civilizacije – od Arhimeda do danas da ljudski rod stigne na svoj cilj jedne opće prirodne zajednice univerzuma. Ipak imamo sreću da nam je prirodan duh zapravo duh dječje radoznalosti – istraživački duh. Stoga je dragocjeno svako rješenje pokraj kojeg obično nehajno prolazimo, iako ono stoji jasno, na prvi pogled neugledno ali transparentno, jednostavno – dok mi, naviknuti na složenost života, tome obično ne vjerujemo – za razliku od djece. Zato ćemo sada djeco, u čast truda svih onih drevnih naroda i u slavu duha znanja i mudrosti, naučiti nešto što ni suvremeni umovi „opijeni vinom visokih tehnologija“ ne znaju, niti žele znati.

Prvo ćemo saznati kako se kocka dijeli na kub 7, dakle 7 x7 x7 konstruirati samo sa šestarom i ravnalom bez mjera, a onda saznati što je to broj pi (Pi) i kako ga nacrtati (geometrijski) po istim pravilima – šestarom i ravnalom bez mjera. A kako sam ja to saznao? Pa, povjerovao sam poput djeteta, ja 60-godišnjak, onom koji se dao raspeti prije 2000 godina. „Pitaj i biti će ti odgovoreno“! Da, u svakom od nas živi dijete – dijete svemira.

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Kub 7 (7³) – Podjela kocke. Uzmemo u šestar neku dužinu i opišemo kružnicu i istom dužinom (radijusom) podijelimo na dijelove – šesterokut, te mu ucrtamo njegov zvjezdasti poligon (svaki drugi pol podjele)

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Nasuprotne polove povežemo dužinama. Dakle, dobili smo kocku (kao u ranijim poglavljima).

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Pri konstrukciji istostraničnog trokuta, stranica veličine radijusa kružnice a saznali smo da njegova visina dijeli kružnicu na sedam jednakih dijelova.

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Rekli smo također da je radijus sedmerokuta manji od radijusa šesterokuta kružnice (više dijelova, manji radijus). Koliko manji? Reći ćemo ovako – i zapamtite: RADIJUS UPISNE KRUŽNICE ŠESTEROKUTA DIJELI OPISNU KRUŽNICU ŠESTEROKUTA NA SEDAM DIJELOVA . (Bitan način za podjelu kocke na kub 7)

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Ucrtali smo radijus sedmerokuta (upisnu kružnicu šesterokuta njegove opisne kružnice). Dobili smo manji šesterokut upisne i ucrtamo ga.

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Sada ucrtamo i manji šesterokutni poligon (zvjezdasti) koji nam sada služi. Tu manju kocku (upisne kružnice šesterokuta opisne) podijelimo na kub 3 (3x3x3).

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Postupak podjele na 3x3x3 naučili smo u prijašnjim poglavljima.

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Kada smo manju kocku podijelili na kub 3, još je jednom podijelimo (a pomoću sjecišta koja su nastala podjelom na tri) na dva dijela – svaki dio (kubni 3) na pola.

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Počinjemo uvijek uz dijametar – okomito – lijevo – desno.

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Takvom podjelom stvaraju se nova sjecišta i točke podjele na bridovima…

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… sve dok konačno nismo podijelili kocku upisne kružnice šesterokuta opisne na 6x6x6 dijelova.

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Kada sada produžimo diobene dužine manje kocke na bridove veće (šesterokutne stranice) opisne , vidimo da smo kocku opisne kružnice podijelili na 7x7x7 dijelova (kub 7) a dijametre opisne kružnice na 14 dijelova.

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Sada možemo 14 dijelova dijametra podijeliti na dva tako da dijametri opsine kružnice imaju 7 dijelova (prikazano). Dakle imamo kub 3,5 (3,5 x 3,5 x 3,5)

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Sada znamo da možemo tu sedminu prikazati (dijametra) i ovako da bi nam lakše bilo prikazati ono zbog čega smo se „mučili“ – prikazati broj Pi (pi).

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BROJ pi (Pi) – RJEŠENJE

Iako se u geometriji crta, objasniti ćemo tako da će svakom biti jasno i svatko će nakon toga moći sam nacrtati broj pi (Pi). Što je pi (Pi)? Kažu beskonačan broj, decimalni pa na kraju je i skraćen na 3,14 (jer tko će računati sa beskonačnim 3,1428571…). Dakle, beskonačan decimalni broj! A zar već ne učimo u drugom dijelu osnovnoškolskog obrazovanja o decimalnim zapisima? Što je decimalni zapis? Pa razlomak je decimalni zapis. A jeste li ikad čuli za beskonačni razlomak? A što su razlomci? Dijelovi. Jeste li ikad čuli za beskonačne dijelove? Naučili smo dobro da su dekadski dijelovi decimalnog zapisa cijeli brojevi, a decimalni dijelovi cijelog imamo kod broja Pi cijeli broj = 3 a decimalni 0,1428571… Pa da vidimo koji je to dio ili razlomak cijelog broja – idemo po redu 1:2 – nije, 1:3 – nije, 1:4 – nije, 1:5 – nije, 1:6 – nije, 1:7 – nije … i gle, to je 1:7 – 0,1428571… =  – jedna sedmina!

I vidi čuda! Broj Pi (pi) je 3 cijela i 1/7 (jedna sedmina). Sada je pitanje čega tri cijela i jedna sedmina. Broj je u geometriji veličina – dužina.

Kada crtamo kružnicu nekog radijusa njenom podjelom radijusom dobili smo šesterokut, šest dijelova, a te dužine koje dijele kružnicu na šest dijelova su tri dužine koje zovemo dijametrima (dvostrukim radijusima jer prolaze kroz središte kružnice od jednog nasuprotnog pola. I sada ako im dodamo tu jednu sedminu dijametra (jednog) dobili smo broj Pi (pi) 31/7 (tri cijela i jedna sedmina) dijametra – 3,1428571.

Kad gle, opet čudo! Ako usporedimo veličinu opsega kruga i zbroj dijametara i jedne sedmine – oni su isti, dakle pi = O ili obratno.

A što je opseg? Opseg je dužina.

Sada znamo kako je nacrtati. Nacrtamo pravac. Odredimo početnu točku. Prenesemo na njega dužine – tri dijametra i dodamo im jednu sedminu. Što smo nacrtali – opseg – broj Pi (pi).

Dakle broj Pi (pi) je dužina opsega kružnice a njegova veličina je 3 cijela i jedna sedmina dijametra te iste kružnice (vrijedi za svaku kružnicu, znanog ili neznanog radijusa).

Prema tome O = Pi (pi)     Pi (pi) = 31/7 = 3,1428571 d

I sada će nam biti lako nacrtati kvadraturu kruga (sljedeće poglavlje).

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6 komentara to “Podjela kocke (kub 7) – Broj π (Pi)”

  1. Ricardo napisao:

    Hello again, I got something important to say about number 7, Admin please give this message to Mr Tomo, because its about a fact about 7 and 5.
    The Circle inside the Hexagon breaks the Main Circle in 7. I agree. I draw it too. Like you say.
    But the radius cant be broken with that circle in 7 like you do in cube of 7. It has to be the Circle that when broken with the radius gives you 5. remember???
    The circle you said I was right about. Its the 3rd time it tells me that something is not right about cube of 7.
    Another exercise I did was the Petal of the Flower of Life. It tells me this:

    D:30 x 26 = Equilateral Triangle side.
    ( diameter divided by 30 times 26) wich relates to what Im about to talk about because the circle of 7 in my opinion breaks the diameter into another number parts…

    D:30×26 for me is more accurate than the D:14×12 you showed me. Just try that equation, it is more accurate ( and yes i know the compass is due to make mistakes, but thats why I drew 50 times the same thing before saying anything) But then I decided to cheat, sort of…. just do diameter of 14centimeters, break radius in 7 with a marked ruler.
    Do circle of less 1/7th of the main radius and then the circle you taught us that is 7 inside hexagon, draw cube, and you will see that it will not hit the hexagon and 7 will, and if you use the radius of our main circle on that smaller circle you get Pentagon with radius sides. You can always do different process, break 1 side of the Cube in 7 with ruler, and then do the exercise you do on top, in this chapter, the 3 cube and alongate those lines. For me they don’t hit right.
    So, something is off in the cube of 7 and more if I am right on this. Only IF….but
    6 of the small cubes are smaller on this drawing you made, the cubes on the corners are smaller than the ones you break inside by a small amount, but that happens, maybe because of our dimensions, they are A4 size, so I made A3 size and this showed up, again.

    I believe that by doing both 7 and 5; IN and OUT of the main circle, tells us the movement or the shifting of their relations. I can sense it, but can’t see it yet.

    How to break diameter into 30 parts?

    I make Star of David and draw all 3 Axis, like you taught us, and then I choose 1 Petal of the flower, and make the biggest possible circle inside the Petal – (This circle has its center point in the middle point of 1 Side of the Triangle – Star of David) I believe you call these 2 sevenths. But Im saying it is 2 fifteenth.
    This circle will make a 15 partition of the diameter, half it to 30, and just drop the lines to the triangle of the star of david and alongate those to a diameter size. Result should be 26 of 30 from the diameter. Meaning; the side of our triangle is 26 parts of a 30 part diameter.
    D:30×26=biggest Triangle Side inside our Circle. And do it in other poligons and on the main circle…and equations are easy to draw, like the one above that I showed for 1 side of the Triangle. Number 30 is a good number in Geometry.

    You say, you use 6cm in A4 paper most often. I prefer 4.4cm as a start in A4 paper, because I think of; 0,6 x 7 and 1\3rd (7,3333…) wich is the opposite of 3 and 1\7 ; in my mind anyway I saw and then I used; I know its crazy, but the results are better in centimeters. and relates to a 0,2 scale of numbers.
    Like 12 = 1,2
    14 = 1,4 so number 2 is 0,2 and 4,4:0,6= 7.3333333….
    I play with symmetry in numbers too. It helps. We must start using measures at some point? Right?
    Also, when you do a new exercise here, I draw them differently right away, 3 or 4 if I have too or more, Quadrature of Circle I made it in 5 or 6 diferent ways, wich is awesome. All I am saying is, you should check these 2 circles I mentioned, because the 144 partition you showed on 12 Chapter is similar to this, the circles are too close to each other when we use small dimensions, to make the 144 correctly I needed better definition, or bigger drawing, and the diference shows there. Zoom in. And Im sure there are others like this, that are close to each other. But this one is a problem for me, because sometimes I get different results when playing with 7. Wrong or right??? Just try it, its a fast exercise and easy to do, I swore I wouldn’t waste your time if I wasn’t sure.
    Thanks for reading. Peace. Thanks

  2. Ricardo napisao:

    Pleaze hear me out on one more thing, about size. It seems that you might be right as well, because I have this feelling that Circles split into 2. You have drawn your cirles at certain size, but maybe when we make it bigger they split, meaning theres a size relation, literally!!, with the circles and relations/dimensions in between, like 1 ring splitting into 2 because they are too far to the eye to see, and when we get close they are actually 2 or more rings and not 1 only…maybe thats whats happening too on my drawings. Cheers!!

  3. Danilo napisao:

    Thanks for this webpage full of knowledge and geometry instruction. I always wanna know the root of the things and geometry is one of them. I was search on the web and found topics about sacred geometry, but always in the religious manner. Here, in your website, I found a pleasent use and clarifyng teach using this spectacular subject.

  4. Vitomir Lalovic napisao:

    Postovanje,
    broj PI nije 3 cela i 1/7.
    Srdacan pozdrav!

  5. satyam napisao:

    Pi is NOT 3+1/7.

    Nor any other fraction. This is well known by decent mathematicians, past & future.

    This is only a crude approximation. Not exact. Stop spreading lies.

    Still don’t understand how to draw exact heptagon : you tell this is, no one can be sure about it (especially given the 22/7 thing).

  6. Ricardo napisao:

    It is 22/7.

    do this Mr.

    65704006445717084572022626334541
    (press square root 6 times) on this number on a calculator.
    the 6th square root of this huge number is your Pi, 3,1415…etc.

    The same as asking, how many numbers exist between 1 and 2…infinite of them, because its an approximation that you dont want to touch or close, or believe its finite, youll get tired of running infinitly.
    They dont account the line thickness of a circle (being part of the area of a circle), on a computer it does the same. A computer should read AREA FORMULA and it reads pixels. You can even say that PI is any number, as long as it is drawn in the same form(SHAPE). I cant get into your mind, but I can make an approximation with words, and use illusions towards your eyes, and all your senses. youll say its true since I fed you up.

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