Zero, and one, and simple addition: this is the starting point of a most adventurous journey through a fascinating series called Fibonacci Series. Fibonacci sequence is a recursive series of numbers where the following number is equal to the sum of the previous two. The sequence goes like, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …. and so on.
Far from being just a mathematical curiosity, however, this sequence recurs throughout nature – from the regeneration patterns of bees to the arrangement of spirals on pine cones and pineapples. All of these are astounding evidence of the deep mathematical basis of the natural world.
There are amazing connections between Fibonacci numbers and natural forms (number of spirals in a pinecone, sunflower seed arrangement). In art, architecture, the stock market and other areas of society and culture one can find an almost endless array of instances where Fibonacci sequence and its derivative the ‘golden ratio’ makes an appearance. There are almost boundless applications of Fibonacci series in geometry, number theory, probability, algebra to name but a few.
Start with a square of 1 unit. Then add another 1 unit suare next to it (0+1 = 1). Next add another square on top of these two so that its length is equal to the sum of the first two squares (1+1=2). Continue adding squares according to the pattern – each new square being equal to the sum of the previous two. This will result in a spiral arrangement of squares of increasing size – a visual, geometric rendering of the Fibonacci sequence.
Spiral created by the Fibonacci sequence is called equiangular and is a common pattern seen in nature.
There is a special relationship between the Golden Ratio and Fibonacci Series. Ratio of any two successive numbers in Fibonacci series is close to the Golden Ratio (1.618025….)
The fabulous Fibonacci numbers demonstrate the beauty of mathematics. The amazing phenomenon permeates just about everything – both in – and outside of the world of mathematics.
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