Za zlatni presek kažu da je najlepša forma. U matematici i umetnosti je specifični odnos između dve veličine koje zadovoljavaju sledeće pravilo: odnos njihovog zbira i veće veličine jednak je odnosu veće veličine prema manjoj.
Zlatni presek se uglavnom obeležava malim grčkim slovom φ .
Matematički izraženo: (a+b)/a=a/b=φ
Sa zlatnim presekom ulazimo u oblast mera, odnosa, proporcija. Da bismo uspostavili bilo kakve relacije, moramo imati najmanje dve veličine. Odnos – „ A prema B “ – označava meru različitosti, poređenje između dve nejednake stvari. Na višim planovima postojanja odnos između dve nejednake veličine se izražava jednostavnom matematičkom formulom: a:b. Rezultat ove proporcije je misteriozni broj , a matematički izraženo to izgleda ovako: Zlatni presek se smatra SAVRŠENOM PROPORCIJOM – Božanskom proporcijom – i matematičari, verujem, imaju čist estetski ugođaj iščitavajući je iz formula. Prevedena na „obični“ jezik ona izgleda ovako: Manje prema Većem kao Veće prema Celini.
ZANIMLJIVOSTI:
Antonio Stradivari (1644 – 1737) koristio je zlatni presek pri izradi svojih gudačkih instrumenata, čiji se savršeni zvuk i danas proučava.
Najveći broj muzičkih kompozicija baziranih na zlatnom preseku nalazi se kod sledećih kompozitora (po Sebanevu): Arsenski (95%), Betoven (97%), Hajdn (97%), Mocart (91%), Skrjabin (90%), Šopen (92%), Šubert (91%). Svih 27 Šopenovih etida, Sebanev je proučavao do najsitnijih detalja. U njima su otkrivena 154 zlatna reza koji nedostaje u svega 3 etide.“
Čuveni Leonardo Davinči je naslikao svoja napoznatija remek dela uz pomoć zlatnog preseka
Listovi na grani rastu na međusobnim udaljenostima, koje odgovaraju FIBONIČIJEVOM NIZU.
Cvetovi najčešće imaju 3, 5, 8, 13, 21, 34, 55 ili 89 latica.
Cvetići, smešteni u glavi suncokreta, razmešteni su u dva niza spirala: jedne u pravcu kretanja kazaljki na satu i druge u suprotnom.
U pčelinjoj zajednici, košnici, uvek je manji broj mužjaka pčela nego ženki pčela. Kada bi podelili broj ženki sa brojem mužjaka pčela, uvek bi dobili broj φ.
Ako izmerimo visinu čoveka od vrha glave do poda, zatim to podelimo sa dužinom od pupka do poda, dobijamo broj φ .
Zlatni presek je u proporcijama lica, ritmu otkucaja srca, strukturi DNA.
Partenon u Grčkoj, egipatske piramide i zgrada Ujedinjenih Nacija imaju proporcije zlatnog preseka
Nautilus (puž mekušac/kućica) u svojoj konstrukciji ima spirale. Kada bismo izračunali odnos svakog spiralnog odnosa prema sledećem dobili bismo broj φ …
Golden Ratio
The golden ratio is a specific ratio between two quantities: the ratio of their sum and the larger of the two quantities is the same as the ratio of the larger and the smaller one.
where
It is widely used in mathematics and art, as well as in architecture. The lowercase of the Greek letter ϕ (phi) is usually used as its symbol. This equation has a unique irrational ratio: The golden ratio is also known as the divine proportion. It is related to the ideal ratio of two quantities. It is often brought in connection with the Fibonacci (Leonardo of Pisa, 1170-1250) sequence, where every number after the first two is the sum of the two preceding ones (0,1,1,2,3,5,8,13…). By dividing each number of the Fibonacci sequence with the preceding number, a new sequence is got, the value of which tends towards the value of the golden ratio. The golden ratio is widely used in architecture and art, particularly in painting, furniture design, fashion, as well as in music, following the human aspiration for perfection.
It is known for at least 2400 years and it has attracted attention of a large number of scientists and artists. Many of them created their works of art following this principle because they wanted to achieve harmony pleasant to the eye of the observer. One of the most famous constructions in connection with the golden ratio is the Parthenon of the Greek sculptor Phidias, built in the 5th century BC. The pyramids are also one of examples. They are still considered as the most harmonious objects of the most beautiful proportion. Since the Ancient Greece, this simple and interesting concept has led numerous scientists to spend endless hours thinking about it. The Greek mathematicians studied it because of its frequent occurrence in geometry. Luca Pacioli described it in his book “De devina proportione” (the Divine Ratio) in 1509. The first known value of the golden ratio was written in 1597 and it was about 0.61803040.
It is believed that Leonardo da Vinci used this method while painting his most famous piece of art – Mona Lisa.
The golden ratio is present everywhere, even in human anatomy. Flower petals, insects’ wings, pattern of sunflower seeds, the shell, and DNA molecule, all these are in connection with it. According to the theory, the whole universe is based on this concept. The logo of the well known “Apple” company was designed using the golden ratio.
