The Story of The Unit Simulacrum and Whole PI

Mending the Sacred Hoop

The Meaning of Whole PI

Chapter Nine – Beyond the Sacred Hoop — Page Six

Fibonacci Ratios

You have seen in Figure 80 and Figure 81 how PI and Phi are related. And you have now seen how Phi and the Unit Simulacrum are related. Now we can relate the Phi Ratio to the Fibonacci Series. If you examine the ratios made by two sequential Fibonacci Numbers, which were shown in the previous section on Continuous Fractions, and are repeated below, you will notice that the Fibonacci Ratios go up and down around a central number.






I created an Excel spreadsheet to calculate the Fibonacci Numbers, by starting with zero and one and simply adding the previous two numbers and continuing down the list, producing each number from the sum of the two previous numbers. Then, I made the ratio of each pair of two sequential numbers, by dividing the smaller number by the next larger number. These ratios pretty quickly converge to the value 0.618033988749895, to 15 decimal places, which is the most that my program allowed. This, of course, is (1/f). This series of ratios started at zero, and quickly converges at (1/f).

Alternatively, the ratios could be constructed by using the next larger number over the smaller number. This creates a series of ratios greater than one, as shown below. Once again, these ratios center around a particular number.

The ratios above pretty quickly converge to the Phi Ratio, f. There is one difference between this series of ratios and the one above that is less than one. The series of ratios that is greater than one that is made from the sequential Fibonacci Numbers cannot have a value of zero. It starts at 1/1. The series of ratios given above shows that when the next larger Fibonacci Number is taken as a ratio over the previous Fibonacci Number, the smaller number cannot be zero, because that gives an irrational number.









The discussion above has described how the Fibonacci Ratios and the Phi Ratio are intimately related. If you construct a spreadsheet yourself, you can confirm the values of the ratios above. There is no reason to take my word for anything. You should convince yourself that what I have shown above is true. You can see for yourself that the ratios above quickly converge to the Phi Ratio. The Fibonacci Ratios are simply the way that nature approximates the Phi Ratio. The Golden Rectangles and the Golden Spiral show how the Phi Ratio construct goes down to infinitely small and up to infinitely large. Nature and physical reality does not know how to handle infinite things, just as we do not know how to fully grasp transcendental numbers. But nature found a way to approximate the pattern of infinity, by using the Fibonacci Series. Now that you have seen the relationship between the Phi Ratio and the Fibonacci Series, and the Phi Ratio and the Unit Simulacrum, there is one more relationship to point out.