West Hartford, CT

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* Fibonacci Numbers* are created by pairwise integer addition. Starting with 0 and 1, it goes like this:

0, 1, then 0+1=1, 1+1=2, **1+2=****3, 2+3=5, and so on.**

So the Fibonacci Sequence is

0,1,1,2,3,5,8,13,21,34,55, . . .

Division of successive **Fibonacci Numbers** converges to the **Golden Ratio**, or 1.618. The inverse of 1.618 is .618. These ratios can be found throughout nature, architecture, art, music and biology. Even some stock market analysts refer to **Fibonacci Reversals **(decline of 61.8% or its complement of 38.2%) in technical analysis of stock patterns.

The proportion of .618 to 1 is the mathematical basis for the shape of playing cards, the Parthenon and Ancient Greek vases. Much of their art and architecture is based upon this proportion.

Renaissance artists Botecelli, Michelangelo and DaVinci called the **Golden Ratio** the *'Divine Proportion' *and used it extensively in their art and architectural masterpieces.

Internet searches will yield much interesting information about Fibonacci Numbers and the Golden Ratio.

* Prime Numbers* are integers that can only be divided by themselves and 1. Many people think that 1 is a Prime, but it is not because, by definition, a Prime needs two

2, 3, 5, 7, 11,13, 17, 19, . . .

(there are an infinite number of Primes however no formula or algorithm has been discovered to generate them)

Prime numbers have been a facination of mathematicians for centuries, since the ancient Greeks and probably before.

**Fibonacci and Prime Boards**

The **Fibonacci Spiral** is comprised of outward expanding squares of **Fibonacci Numbers, **sometimes called * "Nature's Numbering System"*.

Other boards below show the sequences -- either of **Fibonacci Numbers** or **Prime Numbers**.

All of **Fibonacci** and **Prime** boards are scaled in inches divided by 2, 4, or 8 in order to keep dimensions of the boards a usable size.

**Mathematicians and Naturalists may enjoy these boards.**

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West Hartford, CT

forrest