Naslov
The Golden Ratio

Autori
Stipančić-Klaić, Ivanka ; Matotek, Josipa

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), stručni

Izvornik
Proceedings of The 14th International Conference on Geometry and Graphics / Ando, N. ; Kanai, T. ; Mitani, J. ; Saito, A. ; Yamaguchi, Y. - Kyoto : International Society for Geometry and Graphics, 2010, 1-10

ISBN
978-4-9900967-1-7

Skup
The 14th International Conference on Geometry and Graphics(ICGG 2010)

Mjesto i datum
Kyoto, Japan, 05.08.2010. - 09.08.2010

Vrsta sudjelovanja
Ostalo

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Golden Ratio ; Fibonacci ; Golden Triangle ; regular pentagon ; dodecahedron

Sažetak
This paper is about the golden section and the golden ratio. The golden ratio is an irrational number, intriguing and fascinating to mathematicians, philosophers, artist, architects and musicians ever since ancient times until now. The golden section is a line segment divided according to the golden ratio: the smaller part is to the larger part as the larger part is to the whole. It is often marked (or sometime ), because the („phi“) is the first letter in the name of Greek architect and sculptor Phidias whose work often symbolized the golden ratio. We shall give a brief historical review and explore how the golden section and its related concepts appear in architecture with special overview of the application in our region. The golden section was first studied by ancient Greeks because of its frequent appearance in geometry. In his “Elements” Euclid explains a construction for cutting a line “in extreme and mean ratio”, which is Euclid’s term for the golden ratio used until about the 18th century. About 1500s Luca Pacioli published his book “De divina proportione”, it contains drawings made by Leonardo da Vinci of the five Platonic solids and other images of artist, architects and scientists of the golden ratio. The most popular occurrences of the golden ratio in architecture are Parthenon and the Pyramids. But today these are controversial issues ; in the paper that and even more examples of the golden ratio are discussed in architecture. People such as Le Corbusier have deliberately used the golden section in their designs in modern architecture. We shall also explain how to construct the golden section in various ways, found and proved in the works of various mathematicians such as Borsia, Hofstetter, Huntley, Lemoine and Odom. We shall show how the golden ratio appears in an isosceles triangle with a top angle 36˚ and both base angles 72˚ which is usually named “golden triangle”. The same triangle we find out in a regular pentagon and dodecahedron. We shall show an interesting construction of a dodecahedron around a cube, mentioned in Euclid’s Elements, where the golden ratio appears as well. It is also illustrated in this work how the Pythagoreans coped with the concept of incommensurability.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Arhitektura i urbanizam

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