Beginning with 1, line them up in otherwise any way you like. Take any random collection of numbers that includes 1. I liked it too at first, Rachel, but now I realise it's not so exciting after all, since it says nothing about Fibonacci numbers in particular unfortunately. Lastly although I came across these results concerning Fibonacci powers on my own (see also my previous comment about 5), I daresay they aren't new discoveries. For example 13 takes 7 numbers to get to its square, and 13 occupies position 7. Note also the number of numbers in each sequence, which is equal to the position of the start number in the standard Fibonacci sequence. This can be remedied perhaps with: 0 1 1) (My treatment of 1 seems a bit anomalous here since although it 's a perfect square, I haven't presented it as the result of any addition.

In fact the only start numbers we can hit the square with seem to be the Fibonaccis and no others: But then 4 and 6 aren't in the Fibonacci sequence either. The same goes for 6: 6 6 12 18 30 48 doesn't include 36. Try this with 4 however: 4 4 8 12 20, and we don't land on 4 squared. Now let's pretend 5 is the first Fibonacci number instead of the usual 1, but still use the same addition algorithm: 5 5 10 15 25. To find out more read The life and numbers of Fibonacci. The sequence is also closely related to a famous number called the golden ratio. You can find it, for example, in the turns of natural spirals, in plants, and in the family tree of bees. Real rabbits don't breed as Fibonacci hypothesised, but his sequence still appears frequently in nature, as it seems to capture some aspect of growth. And from that we can see that after twelve months there will be pairs of rabbits. Starting with one pair, the sequence we generate is exactly the sequence at the start of this article. Therefore, the total number of pairs of rabbits (adult+baby) in a particular month is the sum of the total pairs of rabbits in the previous two months: Writing for the number of baby pairs in the month, this gives Writing for the number of adult pairs in the month and for the total number of pairs in the month, this givesįibonacci also realised that the number of baby pairs in a given month is the number of adult pairs in the previous month. He realised that the number of adult pairs in a given month is the total number of rabbits (both adults and babies) in the previous month. Fibonacci asked how many rabbits a single pair can produce after a year with this highly unbelievable breeding process (rabbits never die, every month each adult pair produces a mixed pair of baby rabbits who mature the next month).

Fibonacci sequence in nature rabbits