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Fibonacci Fun

The Fibonacci sequence has been mentioned in a previous post, but let’s look at one of the many cool patterns hidden in the numbers.

Just to refresh your memory about the Fibonacci sequence, it appears as follows:  1, 1, 2, 3, 5, 8, 13, 21, …  Each new term in the sequence is found by adding the last two terms.

Now that you have the sequence in your mind, let’s look at a pattern.  Find a number and multiply it with the number following the next.  For instance, if you take 3, multiply it with 8.  The result will always be 1 more or 1 less than the square of the number in between.  So, 3 x 8 = 24 while 5 squared is 25, a difference of 1.  The product is 1 less than the square.  How about we take 5 with 13.  The 8 squared is 64 while 5 x 13 = 65.  Again, there’s a difference of 1.  The product is 1 more than the square.  Whether the result is 1 more or 1 less will alternate down the sequence.  Pretty cool, huh?

The alternating pattern is made all the cooler when you stop to realize that the ratios of successive numbers alternate higher and lower, always approaching phi (the Golden Ratio).

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One response to “Fibonacci Fun

  1. Pingback: Playtime | mathemorsels

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