Every natural number is either a Fibonacci number or it is

Every natural number is either a Fibonacci number or it is

9/15/2012
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
Every natural number is either a
Fibonacci number or it is expressible uniquely as a sum of nonconsecutive
Fibonacci numbers.
Here is one way to find the sum:
1. Write down a natural number.
2. Find the largest Fibonacci number that does not exceed your number.
That Fibonacci number is the first term in your sum.
3. Subtract that Fibonacci number from your number and look at this
new number.
4. Find the largest Fibonacci number that does not exceed this new
number. That Fibonacci number is the second number in your sum.
5. Continue this process.
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2
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http://www.youtube.com/watch?v=fmaVqkR0ZXg
http://en.wikipedia.org/wiki/Golden_ratio
http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=5334&itemId=0470424761&resourceId=18819
3
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http://www.fhperry.com/images/shell.jpg
http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/
4
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http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/
http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/
5