Fibonacci’s book gave the common citizen access to calculation and the ability to record those calculations. Rather than using clumsy Roman numerals, Fibonacci explained how the Indians exploited the numbers 1 to 9 together with the revolutionary new concept of 0 to express numbers efficiently using the place number system. It meant that calculation wasn’t something that was available to the common citizen. But using the abacus required skill and expertise. In Europe, they were still using Roman numerals and the abacus to do calculations. He learnt about these new numbers while travelling in North Africa. His book was meant as an aid to new ways of doing computation and explains the power of the new Hindu Arabic numerals. He did not come to be widely known as Fibonacci until 1853 when the historian Guillaume Libri began referring to him as Fibonacci, the name being short for filius Bonacci (son of Bonacci).įibonacci wrote about these numbers in a hugely influential book called Liber Abaci, published in 1202. The numbers are named after a 13th-Century Italian mathematician from Pisa, also known as Leonardo Bonacci. If a pair of rabbits take a month to mature before it can give birth to a new pair of rabbits, how many pairs of rabbits will there be each month? The answer is in the Fibonacci sequence. If you take squares whose dimensions correspond to the Fibonacci numbers, then it’s possible to arrange them in an expanding rectangle, which explains how they help grow things and why they give rise to spirals.įibonacci also explained how these numbers keep track of the population growth of rabbits. Nature uses what it has grown so far to make the next move. What’s the simplest unsolved maths problem?įibonacci explained that these numbers are at the heart of how things grow in the natural world.The seeds in a sunflower also exploit Fibonacci numbers to pack efficiently. Count the cells on a pineapple, and you’ll find several Fibonacci numbers. A banana has a three-pointed star, an apple a five-pointed star, a persimmon an eight-pointed star. (If it isn’t, that means a petal has fallen off your flower, which is how mathematicians get around exceptions).Ĭut open a fruit, and often you’ll find a star shape with a Fibonacci number of arms. Count the number of petals on a flower and often it’s a Fibonacci number. You find them all over the natural world. © Getty Why are Fibonacci numbers so important? A Fibonacci spiral uses quarter-circle arcs inscribed in squares generated from the Fibonacci sequence. We only know 51 Fibonacci primes, but could there be an infinite amount? The Golden Spiral is a logarithmic spiral, with a shape that is infinitely repeated when magnified. For example, are there infinitely many Fibonacci numbers that are also prime numbers? Like 2, 3, 5 and 13. There are still mysteries about these numbers. There’s a formula for the Fibonacci numbers involving the golden ratio that avoids having to calculate all the previous numbers. If you divide a number in the Fibonacci sequence by the previous number in the sequence (for example, 5/3) then this fraction gets closer and closer to the golden ratio as you take larger and larger Fibonacci numbers. This is regarded by many artists as the perfect proportion for a canvas. It starts phi = 1.61803… It’s defined as the ratio of a rectangle of dimensions A x B where the ratio A/B is equal to (A B)/A. Denoted by the Greek letter phi, it is a number like pi that has an infinite decimal expansion with no patterns. Hidden inside this sequence is another important number in mathematics: the golden ratio. They are the simplest example of a recursive sequence where each number is generated by an equation in the previous numbers in the sequence. So the next Fibonacci number is 13 21 = 34. Every number in the sequence is generated by adding together the two previous numbers.
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