Welcome

 This is a new blog. The title - Money - is an attention grabber. As with most advertising, it has little or nothing to do with the content. We will however, share ideas that may crop up to enhance and/or supplement ones income.

The blog name - fibonacci11 - is more to the point and highlights one of my favourite mathematicians, Leonardo Bonacci.

Over the course of these discussions I would like to dive into the fascinating world of numbers. The Fibonacci sequence has its roots in ancient history. It was not 'invented', it was discovered as it has always existed. How it relates to the 'Golden Ratio' opens volumes of speculation regarding the mathematics of the universe. Just as Pi (3.14159...) relates the diameter of a circle to its circumference, the Golden Ratio, Phi (1.61803..) relates many physical measurements such as the length of phalanges. This discussion can be re-visited later, for now let's get back to Fibonacci.

Essentially the sequence dictates that n+1 equals n plus n-1. In English, this states that the next number in the sequence is equal to the sum of the previous two numbers in that sequence. If we start with the most basic representation, 1, 1 (see how it relates to the blog name?) the next number would be 1 + 1 = 2. The sequence is now 1, 1, 2. Ensuing numbers are 3, 5, 8, 13, 21 and so on. So what? Well, run this out about 20 times:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765

Now take the last number (6765) and divide it by the second to last number (4181)

6765/4181 = 1.61803...

Do it all again with any two numbers (a spreadsheet is useful here)

n1 = 5, n2 = 55 -> n20 = 242875, n19 = 150105 -> n20/n19 = 1.61803...

n1 = 1.23, n2 = 4.56 -> n20 = 22243.68, n19 = 13747.35 -> n20/n19 = 1.61803...

n1 = -7, n2 =3 -> n20 = -5545, n19 = -3427 -> n20/n19 = 1.61803...

And thus the discussion begins.