Is there a magic equation to the universe? Probably not, but there are some pretty common ones that we find over and over in the natural world. Take, for instance, the Fibonacci numbers — a sequence of numbers and a corresponding ratio that reflect various patterns found in nature, from the swirl of a pine cone's seeds to the curve of a nautilus shell to the twist of a hurricane.
Humans have probably known about this numerical sequence for millennia — it can be found in ancient Sanskrit texts — but in modern times we have associated it with one medieval man's obsession with rabbits.
In 1202, Italian mathematician Leonardo Pisano (also known as Leonardo Fibonacci, meaning "son of Bonacci") wondered how many rabbits could come from a single set of parents. More specifically, he posed the question: Given optimal conditions, how many pairs of rabbits can be produced from a single pair of rabbits in one year? This thought experiment dictates that the female rabbits always give birth to pairs, and each pair consists of one male and one female [source: Ghose].
Think about it: Two newborn rabbits are placed in a fenced-in yard and left to, well, breed like rabbits. Rabbits can't bear young until they are at least 1 month old, so for the first month, only one pair remains. At the end of the second month, the female gives birth to a new pair, leaving two pairs total. When month three rolls around, the original pair of rabbits produces yet another pair of newborns while their earlier offspring grow to adulthood. This leaves three pairs of rabbit, two of which will give birth to two more pairs the following month for a total of five pairs of rabbits.
The first Fibonacci numbers go as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and on to infinity. The equation that describes it looks like this: Xn+2= Xn+1 + Xn. Basically, each integer is the sum of the preceding two numbers. This set of infinite sums is known as the Fibonacci series or the Fibonacci sequence. The ratio between the numbers in the Fibonacci sequence (1.6180339887498948482...) is frequently called the golden ratio or golden number. The ratios of successive Fibonacci numbers approach the golden ratio as the numbers approach infinity.
Want to see how these fascinating numbers are expressed in nature? No need to visit your local pet store; all you have to do is look around you.