Home Science Page Data Stream Momentum Directionals Root Beings The Experiment

0. General statements about the structure of numbers0. Introduction

A. Numbers: Counting & Magnitude

B. The Ideal Number

1. The Infinite Continued Fraction and Denominator Series for √2A. Fraction Series for √2

B. Denominator Series for √2

C. The inverse F Series for √2

2. The Infinite Continued Fraction and Denominator Series for √aA. F&D Series for integer square roots, √a

B. Basic Iterative Theorems for integer square roots, √a

C. Generating the D Series for √a

D. The Inverse F Series for √a

3. The Infinite Continued Fraction and Denominator Series for √a/bA. F&D Series for rational square roots, √a/b

B. Square Root Theorems for √a/b

C. Summarizing the discoveries

4. More on the Denominator SeriesA. D Series foundational to the F Series

B. The Geometric Nature of the Denominator Series

C. Every D Series has a Limit

D. A More General Expression for the D Series

5. More on the Infinite Continued Fraction SeriesA. The Difference between consecutive members of the F Series

B. The Raveling of the F&D Series

6. The Slope of the implied Line of the Difference SeriesA. Difference Graphs for √2

B. The conjugates, x and x'

C. Product of Conjugates: x' * x = c = a/b - 1

D. ‘d’, Ratio of conjugates: x'/x = d or the Divine Ratio

E. The Implications of the Divine Ratio and its Graph

7. The Complex Spiral of the Imaginary WorldA. A Computer Experiment

B. Generating the Equation for the Line

C. Equation for a Complex Spiral

D. What does our equation look like?

E. Philosophy: Perspective is everything..

F. This Complex Spiral only a metaphor

G. Review: Special Effects of the Infinite Continued Fraction Family