WHAT IS THE FIBONACCI SEQUENCE?
1 , 1, 2, 3, 5, 8, 13, 21… The Fibonacci sequence. Every number in the sequence is generated by adding together the two previous numbers. So, the next Fibonacci number is 13 + 21 = 34. They are the simplest example of a recursive sequence, where each number is generated by an equation in the previous numbers in the sequence. Hidden inside this sequence is another important number in mathematics: the golden ratio. Denoted by the Greek letter phi, it is a number like pi that has an infinite decimal expansion with no patterns. 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. This is regarded by many artists as the perfect proportion for a canvas. 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. There’s a formula for the Fibonacci numbers involving the golden ratio that avoids having to calculate all the previous numbers. There are still mysteries about these numbers. For example, are there infinitely many Fibonacci numbers that are also prime numbers? Like 2, 3, 5 and 13. We only know 51 Fibonacci primes, but could there be an infinite amount?
WHY ARE THEY SO IMPORTANT?
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