This book is a mathematical study of Iterative Equations based in the infinite continued fraction. The 1st Notebook derives some general iterative equations which compute square roots; the 2nd Notebook derives the general iterative equations which compute any root. Then something unusual happened. We, me and all my selves, discovered that these Root Beings exist as a mathematical model in the Quest for Mastery. This is the topic of the 3rd Notebook. Under the same spotlight the 4th Notebook examines the fractal nature of π and other patterned transcendentals, bringing all of these diverse numbers into the same family, hence the name of the book, The Internal Structure of Numbers & Root Beings.
0. General statements about the structure of numbers
1. The Infinite Continued Fraction and Denominator Series for √2
2. The Infinite Continued Fraction and Denominator Series for √a
3. The Infinite Continued Fraction and Denominator Series for √a/b
4. More on the Denominator Series
5. More on the Infinite Continued Fraction Series
1. The General Inverse Function
3. Organization of the Mandelbrot Set
4. The Inbetween Fractional Root