Fibonacci Numbers as the basis of the wave principle

Elliott stated in Nature's Law that the mathematical basis for his Wave Principle was a number sequence discovered by Leonardo Fibonacci in the thirteenth century. That number sequence has become identified with its discoverer and is commonly referred to as the Fibonacci numbers. The number sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on to infinity.

The sequence has a number of interesting properties, not the least of which is an almost constant relationship between the numbers. 

1. The sum of any two consecutive numbers equals the next higher number. For example, 3 and 5 equals 8, 5 and 8 equals 13, and so on.

2. The ratio of any number to its next higher number approaches .618, after the first four numbers. For example, 1/1 is 1.00, 1/2 is .50, 2/3 is .67, 3/5 is .60, 5/8 is .625, 8/13 is .615, 13/21 is .619, and so on. Notice how these early ratio values fluctuate above and below .618 in narrowing amplitude. Also, notice the values of 1.00, .50, .67. We'll comment further on these values when we talk more about ratio analysis and percentage retracements.

3. The ratio of any number to its next lower number is approximately 1.618, or the inverse of .618. For example, 13/8 is 1.625, 21/13 is 1.615, 34/21 is 1.619. The higher the numbers become, the closer they come to the values of .618 and 1.618.

4. The ratios of alternate numbers approach 2.618 or its inverse, .382. For example, 13/34 is .382, 34/13 is 2.615.