Natural Fibonacci Numbers and Others
Natural Fibonacci Numbers
The Fibonacci number series starts with 1, 1, 2, 3, 5, 8, 13, 21, 34. The ratio between adjacent numbers in this series after 21/34 is .618 plus many other numbers. The Fibonacci number series that starts with 1, 1 could becalled the natural series since in nature it would start with 1.
Other Fibonacci Numbers
Any number could be the start of a Fibonacci number series since the series is started by adding zero to a number (FN) twice and continued by adding together the two previous totals. The natural Fibonacci series tells us how many times the original number (FN) each new total will be when the series does not start with one.
1xFN, 1xFN, 2xFN, 3xFN, 5x FN, 8xFN, 13xFN, 21xFN, 34xFN
Since the series has this form, the ratio between adjacent numbers in the series will be .618 (plus many other numbers not the same ones as the natural Fibonacci series) from the ninth number, 34x FN, in the series on.
Before that the ratios would be the same as in the natural Fibonacci series 1/2, 2/3, 3/5, 5/8. 8/13, 13/21. These ratios are said to be tending toward .618 but really they are themselves - the description of the ratio between the number of times the FN is occurring. After the ninth number the ratio never changes.
So if , in nature, a form began with a large number of cells present - a branch from a stem perhaps - it still would take on the Fibonacci ratios if in cell division the two previous numbers were ADDING together.
The Fibonacci number series starts with 1, 1, 2, 3, 5, 8, 13, 21, 34. The ratio between adjacent numbers in this series after 21/34 is .618 plus many other numbers. The Fibonacci number series that starts with 1, 1 could becalled the natural series since in nature it would start with 1.
Other Fibonacci Numbers
Any number could be the start of a Fibonacci number series since the series is started by adding zero to a number (FN) twice and continued by adding together the two previous totals. The natural Fibonacci series tells us how many times the original number (FN) each new total will be when the series does not start with one.
1xFN, 1xFN, 2xFN, 3xFN, 5x FN, 8xFN, 13xFN, 21xFN, 34xFN
Since the series has this form, the ratio between adjacent numbers in the series will be .618 (plus many other numbers not the same ones as the natural Fibonacci series) from the ninth number, 34x FN, in the series on.
Before that the ratios would be the same as in the natural Fibonacci series 1/2, 2/3, 3/5, 5/8. 8/13, 13/21. These ratios are said to be tending toward .618 but really they are themselves - the description of the ratio between the number of times the FN is occurring. After the ninth number the ratio never changes.
So if , in nature, a form began with a large number of cells present - a branch from a stem perhaps - it still would take on the Fibonacci ratios if in cell division the two previous numbers were ADDING together.
posted by wildswan at 9/13/2006 03:22:00 AM
0 Comments:
Post a Comment
<< Home