Fibonacci Discovers a Pattern

While averages settle into a number that’s lower than the highest in the series and higher than the lowest, other sequences involving three numbers expand.  Threes can be represented by relationships of two things to a third in a sequence that’s additive and infinite.  The Fibonacci series, for example, is a sequence of sums.  Starting with 0, add 1 to equal one.  0 + 1 = 1.  Then add the two preceding numbers.  1 plus 1 equals 2.  Add 1 and 2 to equal 3.  Two plus three equals five, and so on.  The series rolls out like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, etc. 

Fibonacci numbers were named after Leonardo of Pisa (c. 1170-c. 1250) who was known as Fibonacci.  He published a book on mathematics in 1202 that described the series, although it had originated in India several centuries before.  Fibonacci found examples of the series in nature.  One of his first studies was the creation of the sequence of individuals from a single pair of adult, mating rabbits.  He concluded, given the parameters of his study, the rabbit pairs would multiply in accord with the numbers in the series identified with him.  Fibonacci numbers are used in financial markets today to make predictions about the movement of prices. 

From Threes, Chapter 2, “Threes in Math”