http___fractalenlightenment.com_15668_fractals_digging-deeper-into-the-golden-ratio_1.xml
http___fractalenlightenment.com_hr_15668_fractals_digging-deeper-into-the-golden-ratio_1.xml
1.1 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 4.1 5.1 5.2 6.1 6.2 6.3 7.1 7.2 7.3 7.4 8.1 9.1 9.2 10.1 10.2 10.3 11.1 12.1 13.1 14.1 14.2 15.1 15.2 16.1 16.2 16.3 16.4 17.1 18.1 19.1 20.1 20.2 20.3
Digging Deeper into the Golden Ratio The golden ratio, or the divine section, A+B:(A+B)-B or (A+B)/A, represented by phi and it’s ratio to one. Occurs when the ratio of two numbers equal their sum. As is, as to. Everything follows the pattern that created it, in mathematics, and in nature. The true golden ratio is a ratio applicable for determining the past, present, and future states of any pattern, even outside of numbers. It is believed that this ratio is everywhere in nature. Over 2300 years old, perhaps this is the reason we find the golden rectangle, a rectangle whose shorter side is as to the golden ratio to the longer side, aesthetically pleasing? Perhaps aesthetic pleasure occurs when the brain witnesses the pattern it is most familiar with, when nature views it’s reflection. A synopsis of the Golden Ratio Its the gold standard of ratios! A golden ratio, also known as a golden section, golden mean, and divine proportion is related to fibonacci’s sequence of numbers. Mathematicians as old as Euclid studied it’s appearance in the regular pentagon and the golden rectangle. In a pentagon, the area is one half the perimeter multiplied by the apothem. Here the golden ratio can be illustrated through the five fold symmetry of the pentagon, the apothem represents B and any side of the pentagon is A, as to the golden ratio. The golden ratio was also studied by Greek mathematician Pythagoras. The Pythagorean theorem, a² + b² = c², as to the golden ratio, a as to c² and c, as a² + b². The Pythagorean theorem arises from the value of phi, the only number that’s square is one more than itself. Illustrated by 1+√Φ=Φ, a²+b²=c², 1+2=3. Optical Tricks of the Parthenon However it goes back even further as far as the history of civilized man. It is known that dimensions of pi and phi were used in the construction of the great pyramids of Giza. Supposedly the great pyramid’s base is 230.4 meters, as to it’s height, 146.5 meters, are at a golden ratio, forming golden triangles at the pyramid’s sides. It’s surface ratio is also analogous to that of the golden ratio. Geometrically the great pyramid can also represent pi, the difference of a circles radius to it’s circumference. These things may not seem very significant, but one could reach an understanding of these rates and ratios past the numbers once it is known that the great pyramids existed before civilized man even had recorded documents of the values or even the numbers themselves for pi, and phi, yet they appear almost perfectly in these huge megalithic archaeological structures. Does this suggest that the meaning of these rates and ratios is beyond the perfect math we use to understand and represent it? Dr. Daniel Lordick – Architectural Fractals Structures of stochastic self-similarities can sometimes be found in architecture. Frequently mentioned examples are Gothic cathedrals, the Eiffel Tower, and a class of Indian temples. If you understand the truth of the golden ratio behind the mathematics, as the application that is self applicable to everything, even determining the past, present, and future states of any pattern. By plotting the points of a pattern, a system emerges, this system could be used to determine the value of it’s future iterations. For example, if one is valued by two halves of 0.5, then two equals fourths of 0.5, and three equals sixths of 0.5. In time, and quantum wave physics, with the partial momentum of any object you can determine total velocity. The ratio illustrates how our perception of reality is determined by a higher awareness of what reality is. Everything becomes as to what it has become. Resources: Golden Section in Art and Architecture Comments Thanks for all the work you put into fractal enlightenment. It is appreciated. Peace n LOVE.
1.1 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 4.1 5.1 5.2 6.1 6.2 6.3 7.1 7.2 7.3 7.4 8.1 9.1 9.2 10.1 10.2 10.3 11.1 12.1 13.1 14.1 14.2 15.1 15.2 16.1 16.2 16.3 16.4 17.1 18.1
Kopanje dublje u zlatnom rezu Golden ratio, ili bo, B:( B)-B ili ( B)/A, zastupa fi i to je omjer na jednu. Javlja se kada je omjer izme?u dvaju brojeva jednak njihov zbroj. Kao , kao. Sve , iz matematike, i u prirodi. Istina zlatni omjer je omjer primjenjiva za odre?ivanje pro, prisutan, i budu?e dr, i izvan brojeva. Smatra se da je taj omjer je svugdje u prirodi. Više 2300 stara godina, možda je to razlog zbog kojeg smo pronašli zlatni pravokutnik, pravokutnik čija je kraća strana je što se tiče zlatnog omjera na dužoj strani, estetski ugodan? Možda estetski užitak događa kada svjedoci mozga uzorak to je vrlo upoznat s, kada se pogleda priroda je odraz. Sinopsis Zlatnog Ratio Njegov zlatni standard omjera! Zlatni rez, također poznat kao zlatno dijelu, zlatna sredina, i božansko udio se odnosi na Fibonacci je slijed brojeva. Matematičari stara kao Euclid studirao je nastup u regularnom peterokuta i zlatnog pravokutnika. U peterokuta, Područje je jedna polovica opseg pomnožen apothem. Ovdje zlatni rez se može ilustrirati kroz pet puta simetrije peterokuta, apothem predstavlja B i svaka strana peterokuta je, što se tiče zlatnog omjera. Zlatni rez je također studirao grčki matematičar Pitagora. Pitagorin poučak, a² + b² = c², što se tiče zlatnog omjera, da c² i c, kao a² + b². Pitagorin poučak proizlazi iz vrijednosti fi, jedini broj koji je trg je jedan više od sebe. Ilustrirana za 1 √Φ = Φ, a² b² = c², 1+2= 3. Optički trikovi Partenona Međutim to seže puno dalje što se tiče povijesti civiliziranog čovjeka. Poznato je da su dimenzije pi i fi su korišteni u gradnji velikih piramida u Gizi. Navodno je Velika piramida je baza 230.4 metara, da je visina, 146.5 metara, su u zlatnom omjeru, oblikovanje zlatne trokute na piramide strane. To je omjer površina je analogan onome zlatnog omjera. Geometrijski velika piramida također može predstavljati pi, razlika od krugova radijusa bi to opseg. Te stvari ne može činiti vrlo značajan, ali moglo bi doći do razumijevanja ovih stopa i omjerima posljednjih brojeva nakon što se zna da su velike piramide postojala prije civilizirani čovjek, čak je imao snimljene dokumente vrijednosti ili čak samih brojeva za pi, i fi, ali oni se pojavljuju gotovo savršeno u tim ogromnim megalitskih arheoloških struktura. Znači li to sugeriraju da značenje tih stopa i omjerima je izvan savršene matematiku koristimo razumjeti i predstaviti ih? Daniel Lordick – Arhitektonske Fraktali Strukture stohastičkih vlastitih sličnosti ponekad može naći u arhitekturi. Često se spominju primjeri gotičke katedrale, Eiffelov toranj, i klasa indijskih hramova. Ako ste razumjeli istinu o zlatnom omjeru iza matematike, kao program koji je samostalno primjenjuje na sve, čak i utvrđivanje prošlost, prisutan, i budu?e dr. Ucrtavanjem točke uzorkom, Sustav pojavljuje, ovaj sustav može se koristiti za određivanje vrijednosti je buduća ponavljanja. Na primjer, ako se vrednuje po dvije polovice 0.5, zatim dva jednaka četvrtine 0.5, a tri jednaka šestina 0.5. Na vrijeme, i kvantna fizika val, s djelomičnim zamah kojeg objekta možete odrediti ukupnu brzinu. Omjer pokazuje kako je naša percepcija stvarnosti određuje višoj svijesti o tome što je stvarnost. Sve postaje kako bi ono postalo. Sredstva: Zlatni rez u umjetnosti i arhitekturi