I have a question or rather a query to ask. We are giving our son (year 8, 12 yrs old) a little extra tuition at home in maths and general things because we feel the school is not really focusing on the basics. But then maybe it is our son, but the general feeling is much the same through parents at our school, seems to be this particular year and maybe more has missed out, and we are concerned as they go to college (Yr 9 up) next year that they will not cope. The school does not believe in any kind of testing, exams for evaluation, what needs working on etc... and last year when the yr 8 came to sit their test / exam for college it was a complete shock, not only the questions but the how to sit an exam. It is a smaller school in New Zealand (Yr 1 to Yr 8).

We have been doing pattern finding with him, talking to a friend he mentioned the "Fibbinacci Series" ?, while I have tried to find a bit about it, how works etc.. what it is about, I have not really found out much, what I have I feel is way beyond him, but am still curious to know the basics of it myself. Would you be able to tell me in laymans language. Would be very much appreciated. Thankyou.

Regards Shona

Hi Shona,

I start off with a biographical note on Fibonacci:

"Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller.

Did his countrymen wish to express by this epithet their disdain for a man who concerned himself with questions of no practical value, or does the word in the Tuscan dialect mean a much-travelled man, which he was?"

This comes from the information on Fibonacci at the MacTutor History of Mathematics archive, The Fibonacci sequence comes from a problem on rabbits, in Fibonacci's book Liber abbaci:

"A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?"

The solution is found by computing how many pairs of rabbits are there at the end of each month. The first month there is one pair as we are told. The second month there is still only one pair, because it takes two months to become productive. At the end of the third month, we find two pairs of rabbits: the original pair and the first pair it "produced". The next month, we find three pairs, because the original pair has produced a new pair, while the other pair is not productive yet. The month after that, things get more complicated, because there are now two pairs of productive rabbits yielding offspring, and this number will grow. To keep our numbers straight, we use the general formula:

Number of pairs of rabbits next month = Number of pairs of rabbits this month + number of pairs of rabbits last month.

(where the second number counts the number of rabbits that will be productive and will yield offspring next month). This shows that the month after you had 3 pairs of rabbits, you get 5, and then 8, and so on. The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... is called the Fibonacci sequence. Each new term is obtained by adding the previous two; It counts the number of pairs of rabbitsthat you have at the end of each successive month according to the data of the problem.

It is interesting to note that this kind of "recursive" computation has many important applications nowadays in computer science, but it started out 800 years ago as a puzzle to solve just for fun.

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