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Wednesday, August 20, 2008

Fibonnaci Again

Some facts are instances of a Great Principle, while others Just Are. Here is a nice example I take from a book by Martin Gardner, the great popularizer of math and science--Mathematics Magic and Mystery (Dover, 1956):

Write down the first ten terms of any Fibonacci sequence, e.g.: 7,2,9,11,20,... Their sum is 11 times the 7th term. This is easily proven by brute force: 1st term a, 2nd term b, 3rd term a+b, 4th term a+2b, etc. The sum of the first ten terms is 55a+88b; the 7th term is 5a+8b.

This just is. Examine the first few terms of ths sequence and you will not find more instances of like behavior.

What does philosophy have to say about this sort of thing, I wonder?

2 comments:

  1. scineram5:25 PM

    "Examine the first few terms of ths sequence and you will not find more instances of like behavior."

    Proof?

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  2. That was not intended as a math statement, merely as a human observation, viz., if you actually look at the first few terms--say, 10--you will not see any other similar relationship between any of the terms and any of the sums--at least, not if you are remotely like me in the way your mind works.

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