Labor Day Fun Facts via Leonardo Fibonacci da Pisa

• Posted by Greg Harmon
• on September 2nd, 2013

Many are aware of the Fibonacci sequence (above) and Golden Ratio, or Φ, made known by Leonardo from Pisa (yes the town with the leaning tower). Some also understand some properties of the Golden Ratio, like 1.618 = 1/0.618. But there’s all sorts of fun you can have with the Fibonacci numbers and sequence. Why not pick up a few tidbits to impress your friends at that Labor Day Barbecue. For example did you know:

1. No 2 Fibonacci numbers in succession have common factors.

2. If you order the Fibonacci numbers 1,1,2,3,5,8,… as 1,2,3,4,5…. that with the exception of the 4, whenever the order number is prime the Fibonacci number is also prime.

3. The sum of any 10 Fibonacci numbers is divisible by 11.

4. 1 added to the sum of all Fibonacci numbers up to any point equals the Fibonacci number 2 places higher.

5. The sum of consecutive squares starting from the first number (1) will always equal the product of the last number in the sequence times the next number in the sequence.

6. The square of any Fibonacci number is equal to the product of the number in the sequence before and after it, plus or minus 1. The plus or minus alternates along the sequence.

For the more visually inclined, the short video below by Cristobal Vila about finding the Fibonacci Sequence and math in nature is wonderful. I think I have watched it about 25 times. Oh and it has a Dragonfly in it.

The fun facts above are from Elliott Wave Principle by A. J. Frost and Robert B. Prechter, Jr.
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