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FIBONACCI NUMBERS
The Fibonacci sequence is one of the most famous sequences in
both the world of maths and the world in general. The first
fifteen Fibonacci numbers are:
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
Answer the following questions as the basis for your
investigation and presentation.
1. How is the Fibonacci sequence made?
2. What sort of number is every third term? (And therefore
what sort of numbers are every first and second term?)
3. Choose any three consecutive Fibonacci numbers.
Multiply the first by the third. Square the second. Repeat
this for other groups of three. Write what you notice.
4. Choose any four consecutive Fibonacci numbers. Multiply
the first by the fourth. Multiply the second by the third.
Repeat for other groups of four. Write what you notice.
5. If T1 = the first term, T2 = the second term, T3 = the third
term and so on:
a) Find the sum of the first four terms. Compare the total
with T6.
b) Add the first five terms. Compare the total with T7.
c) Add the first six terms. Compare the total with T8.
d) Without adding, find the sum of the first 12 terms.
Look at questions 2,3 and 4. Can you prove them? If yes, how
do you think you can prove that it is always the case?
Research some additional information about Fibonacci for your
presentation. Who was he? Give us some background
information about him as a man.
Also, can you find out for us some famous maths problems that
involve the Fibonacci numbers? (HINT: There are loads!!)
The Fibonacci sequence is often referred to as “Nature’s Code”.
Can you give us examples of where in nature the Fibonacci
sequence can be found?