golden ratio

overview of golden ratio

What is the Golden Ratio?

Closely related to the Fibonacci Sequence (which you may remember from either your school maths lessons or Dan Brown's The Da Vinci Code), the Golden Ratio describes the perfectly symmetrical relationship between two proportions.First described in Euclid’s Elements 2,300 years ago, the established definition is this: two objects are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The value this works out to is usually written as 1.6180First described in

application

The most famous application of the golden ratio is the so-called golden rectangle, which can be split into a perfect square, and a smaller rectangle that has the same aspect ratio as the rectangle it was cut away from. You can apply this theory to a larger number of objects by similarly splitting them down. The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron.

world art

In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it. The Golden Ratio is also sometimes called the golden section, golden mean, golden number, divine proportion, divine section and golden proportion.

Does the golden ratio exist in nature?

The term "golden section" (in German, goldener Schnitt or der goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol phi ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). Similarly, the alternate notation tau is an abbreviation of the Greek tome, meaning "to cut." Though people have known about phi for a long time, it gained much of its notoriety only in recent centuries. Italian Renaissance mathematician Luca Pacioli wrote a book called "De Divina Proportione" ("The Divine Proportion") in 1509 that discussed and popularized phi, according to Knott.

Pacioli used drawings made by Leonardo da Vinci that incorporated phi, and it is possible that da Vinci was the first to call it the "sectio aurea" (Latin for the "golden section"). It wasn't until the 1800s that American mathematician Mark Barr used the Greek letter Φ (phi) to represent this number.

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