![]() ![]() That is, Phi is a geometric construction (concerning the properties of figures) that occurs as follows: Phi shown as a line divided in two segments, a and b, so that the whole line (a+b) is to the longer segment a the same as a is to the shorter segment b φ = (a+b)/ a = a/ b / Image: Wikimedia commons The golden number, represented by the Greek letter Phi (Φ,φ), is derived from this succession, and expresses the relationship between two segments of a straight line. The series discovered by the mathematician from Pisa (0,1,1,2,3,5,8,13…) falls within the field of arithmetic(it studies the numbers and the elementary operations that can be done with them). The Fibonacci succession and the golden number are two sides of the same coin. That said, however, we need to turn to the Italian’s discovery if we want to learn more about the potential harmonious capacity of Phi and its derivatives. ![]() So Phi was neither discovered by Fibonacci (it had already been defined and studied by Euclid), nor owes its name to the Italian. This was why the American mathematician Mark Barr decided to honor him by giving the symbol Φ his initial in Greek ( Phi). According to Mario Livio in his book “ The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number”, certain historians maintain that Phidias successfully used the golden ratio in his works. Phi (Φ,φ) is called Phi after the famous Greek sculptor Phidias (5th century B.C.), the creator of towering architectural landmarks like the Parthenon in Athens. Does this mean it’s possible to find a numerical translation for everything we see, hear or build around us? Perhaps the closest answer to this question is the phrase by Plato that opens this article.īut let’s take a closer look at a mathematical phenomenon that has attracted the attention of thinkers from all disciplines and periods since it was discovered: the golden ratio or the divine proportion. Before we start, we must go all the way back to the story of the mathematician Leornardo Bigollo (Leonardo Pisano or “the one from Pisa”), Fibonacci. You’re very likely to have come across it in any of these disciplines. Nor is it unknown to lovers of art, biology, architecture, music, botany and finance, for example. ![]() Phi (Φ,φ) –the golden number or Fibonacci’s number– is a very familiar concept, and one that has been studied by mathematicians of all ages. 1571-1630), another German mathematician.“God geometrizes continually”, Plato (427-347 B.C.). The interesting thing here is that a German mathematician Simon Jacob was the one who noticed that consecutive Fibonacci numbers converge to the golden ratio.Īs you can notice, a given number equals the sum of the previous two consecutive numbers and therefore the golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as it was discovered by Johannes Kepler (c. īy the way, Leonardo Da Vinci (1452 - 1519) who illustrated Luca Pacioli’s book, Divina proportione (1509), called the golden ratio as section aurea (golden section) and used this proportion or ratio in many of his paintings and works. He used the golden ratio in related geometry problems, though never connected it to the series of numbers named after him. 1170- 1250) also known as Leonardo of Pisa or Leonardo the Traveller from Pisa popularized the Hindu-Arabic numeral system in the Western World. ![]()
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