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Fibs
The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
Paving Paths
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
Gnomon Dimensions
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
Age 11 to 16
Challenge Level
Beginners to LOGO programming may want to start by working through the FIRST FORWARD series of introductory articles before tackling this problem.
Below are some examples of recursion. I had been trying to replicate the spirals within the head of a sunflower!
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The program used was:
TO SUNF :S :A
FD :S RT :A
SUNF :S + 1 :A
END
You might like to replicate the spirals above by considering suitable values for the variables :S and :A.
The real challenge is to simulate the head of a sunflower with more spirals that are much more tightly packed and look distinctly more 'Fibonacci' in proportion!
NRICH is part of the family of activities in the Millennium Mathematics Project.