What's the next number in this sequence: 1, 1, 2, 3, 5, 8, 13, 21...? Anyone who has read Dan Brown's The Da Vinci Code will know that the answer is 34. The sequence is one of the first codes that readers are challenged with in the thriller. Even if you haven't read Dan Brown, spotting the underlying pattern is not too difficult. You get the next number in the sequence by adding together the two previous numbers. So 5+8 gives you 13, for example.

These are some of Nature's favourite numbers. They can be found all over the natural world. Take a pineapple and count the number of cells climbing up the side of the fruit, then count down one of the other spirals and you'll find two numbers in the sequence. Count the number of petals on a flower and it is nearly always either one of these numbers or twice one of these numbers (some flowers are built as if they are two flowers, one on top of each other).

The sequence is named after the great 13th-century Italian mathematician Fibonacci, who spotted the importance of the sequence when he was investigating how the number of rabbits evolves from one generation to the next. But he wasn't the first to reveal the importance of these numbers - a 6th-century Indian poet called Virahanka was perhaps the first to single them out as significant. Virahanka discovered that these numbers count rhythm patterns.

Virahanka was interested in rhythms that you can make out of long and short notes. A short note lasts one beat, while a long note lasts two beats. For example, how many rhythms can you make that are four beats long by making different combinations of short and long beats? You could do short, short, short, short, or long, long, or short, short, long, or short, long, short, or, finally, long, short, short. That's five different rhythms.

If you now analyse the number of rhythms with five beats, you'll get eight different rhythm structures, the next number in the Fibonacci sequence.

The connection with the Fibonacci sequence becomes clear when you realise that, if you want the number of rhythms with N beats, then there are two ways to get them: take the rhythms with N-2 beats and add a long note; or take the rhythms with N-1 beats and add a short note. The total number of rhythms therefore consists of simply adding the two previous numbers in the sequence together.

These numbers have not only obsessed Indian poets, Italian mathematicians and thriller writers. Similar sequences of numbers are at the heart of Le Corbusier's theory of Modulor architecture.

Le Corbusier recognised that these numbers were related to proportions in the human body and believed that the vibrancy of a building depended on capturing proportions in human forms. But there was another reason why he was drawn to these numbers. Hiding behind all these sort of sequences is a very important number in theory of aesthetics: the golden ratio.

Consider the fractions that you can make by dividing one number in the sequence by the previous number. For example, with the Fibonacci sequence we get a list of fractions: 1/1, 2/1, 3/2, 5/3, 8/5 ... Then, as you work your way through these fractions, they get closer and closer to this special number called the golden ratio, which starts 1.61803 ... and then, like pi, the decimals go on for ever without any pattern. The golden ratio is considered by many to be the perfect proportions in art and architecture. The proportions of the Parthenon are typically meant to capture this mathematical ratio. The fractions built from Le Corbusier's numbers also home in on the golden ratio.

But despite being studied for more than 1,000 years, these numbers retain many mysteries. For example, is there an infinite amount of prime numbers in the Fibonacci sequence? Mathematicians know that every Fibonacci number that is not in a prime position in the list cannot be prime. For example, the sixth Fibonacci number is 8, not prime. So if a Fibonacci number is prime, it must be in a prime position. For example, 13 is prime and it's the seventh Fibonacci number. But unfortunately, if we look at a Fibonacci number in a prime position it doesn't always give a prime.

It is still a mystery whether you can get infinitely many Fibonacci primes. But then mathematics would be boring if we knew all the answers.

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