These fractions have the value of the golden ratio. To be ‘golden’, (a + b)/a must equal a/b. The part of the rectangle that remains will itself have sides whose lengths are proportionate to the golden ratio. This is obvious if you take the ‘golden rectangle’ (image below) and divide it according to the golden ratio. One is the self-similarity property of the golden ratio. As simple as it may sound, the implications of such a definition are profound. Through this article, let’s examine some historical arguments associated with the Fibonacci series, the golden ratio and their relationship – and to claims about work on these concepts by scholars in ancient India.Ī line is said to be divided in the golden ratio if the ratio of the larger to the smaller part is as the whole to the larger part. The Fibonacci series also occurs throughout nature, like in the arrangement of certain seed patterns. You can obtain the Fibonacci series by taking two initial numbers, say 0 and 1, and then calculating the next term by adding the two previous terms. The Fibonacci series is one of many interesting topics in mathematics, most importantly for its association with the golden ratio, which has a lot of peculiar properties and an equal number of myths related to it. Many indocentric claims about the Fibonacci series and the ‘golden ratio’ in mathematics don’t do justice to the actual history of the subject – while the proponents of these claims almost always exaggerate their assertions to a point where many original innovators don’t get their due credit. More often than not, such claims are used to float deceptive conclusions about how ancient Indian scholars knew these concepts and their applications.It is easy these days to find articles and social media posts claiming to analyse the relationship between the Fibonacci series and golden ratio, and thereon to Indian culture.Many indocentric claims about the Fibonacci series and the ‘golden ratio’ in mathematics don’t do justice to the actual history of the subject.Photo: Max Ronnersjö/Wikimedia Commons, CC BY-SA 3.0 A detail of an Aeonium tabuliforme plant from Gothenburg, Sweden, displaying a Fibonacci spiral pattern.
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