Subject Outline

This SUBJECT OUTLINE acts as a table of contents with links to every text page. The TUTORIAL MENU in the upper-left frame is a selection of pages suggesting a sequential reading. Pages marked with a glassy blue bullet in this SUBJECT OUTLINE are also listed in the TUTORIAL MENU. Not every page will predefine the terms that it uses, but a glossary has been provided with text-links to it.
Between autumn of 1993 and November of 1997 I worked on approximation methods for finding the partial solutions of polynomials with real number roots. This self- educative search was inspired by a hieroglyphic in a tomb of one of the Ramses' Pharaohs depicting both the Pythagorean theorem and the golden ratio. What followed was an almost constantly evocative continuum of eurekas! as I combed the literature available at the UCLA research libraries and fabulously rich in esoteric literature library of Cal. State U. at Northridge and dreamed up thought experiments in DOS Q-Basic. [Remember that earthquake back in January of '94?, well I worked on the computers at CSUN's library up to Christmas eve '93 and then avoided work both before the quake when the library reopened after the holidays as well as after the quake while languishing in depression for awhile; I also used to sleep between classes in my car on the bottom floor of that parking structure that collapsed 'cause it was cool there in the summertime!, the upper floors would wobble every time a car would pass behind me! oh well...] I also wrote texts devoted to my conclusions and results. I had been hoping to write a book on the subject, but every time I made an attempt, I would rewrite some of the previous chapter attempts as well as write some new ones. So I gave up thinking a solid book would ever materialize. Then along came greater public awareness of the internet and its potential to create an electronic book with updateable text seemed such a cool idea. But it seems I got lazy and never bothered to attempt much other than a scanty series of overview and conclusion pages. But languish no more. Here is a file linking all of those text files and Q-Basic program files. Peruse at your leisure....

Math Section

0. Introduction 1. Logic A. Logic Flow B. Logic Base C. Prime Factorial of Bases D. Base Two Logic I. The Logical Structuring of Mathematical Functions II. Dividing by Infinity and Zero a. The Theory: i. Version 1 ii. Version 2 b. A Case Example E. Base Six Logic I. Imaginary Numbers 2. Polynomials in One and Multiple Unknowns A. Formation and Identity B. Complete Solutions C. Averaging Methods I. Plotting the Error of a Function: "Best Fit" D. Partial (Approximate) Solutions I. Isolation of Terms a. Continued Coefficients i. Substitution ii. Looping Formula iii. Serial Progresion b. Continued Radicals c. Continued Fractions i. Ratios 1) Incremental Progression 2) Euclidean Algorithms A) Quadratic Derivation B) Golden Extention C) Cubic I) Transformative a) Long Version b) Short Version D) Quartic (4^th degree) and Beyond ii. Numeric 1) Square Roots of Numbers 2) Transcendental Numbers, one example A) Approximation of: /4 I) The Source a) Gauss's Version b) Forcing a Coefficient to Unity when it is Associated with the x¹ Term II) Accuracy Testing d. Mixed Continued Radicals with Fractions: Approximating the Roots of Polynomials i. The Partial Solution of: a × (xⁿ - b = 0), for "n" as any Positive Integer, Using Only a Credit Card Calculator: Seeking the Root of a Positive Number ii. Newton's Averaging of Partial Solutions II. Coefficient Methods a. x⁰: Pseudo-Geometric Progression b. x^degree: Summation of Powers of Quadratic Roots i. Fibonacci ii. Lucas 3. Aesthetic Mathematics (some of it anyway) A. The Golden Class I. Regular Polygons a. Chords b. Isosceles Triangles c. Roots of Golden Polynomials d. Odd-Sided Polygons: Beauty i. Golden Beautiful Polynomials are, for the most part, Irreducible e. Even-Sided Polygons: Power, (Semi-Golden) i. The Reduction Of Golden Powerful Polynomials ii. The Sacred Class 1) Ratio Hybrids of Golden Power Roots 2) Geometry A) Two-Dimensional I) Special Case: The Octagon II) All Others... B) Three-Dimensional I) Platonic Solids 3) A Parallel Demonstration (possible indication for a proof) for the Degree-Polynomial Reducibility Formula (Author Unknown, though famous---need help with identifying him): The Restricted Case of: For all N as non-negative Integers [0, 1, 2, 3, ..., ]: 2^{(2^N-1)} = the degree that is required of any polynomial for that polynomial to be reducible (completely factorable) when all of its roots are irrationally real and all of its coefficients are present (non-zero). Examples: a) 1^st Degree = 2^{(2^0-1)} = 1, i.e.: x¹ - 1 b) 2^nd Degree = 2^{(2^1-1)} = 2, i.e.: x² ą x - 1 c) 8^th Degree = 2^{(2^2-1)} = 8, i.e.: x⁸ ą x⁷ - 7x⁶ 6x⁵ - 15x⁴ ą 10x³ - 10x² 4x - 1 d) 128^th Degree = 2^{(2^3-1)} = 128, i.e.: x¹²⁸ ą , ..., ą x - 1 e) 32,768^th Degree = 2^{(2^4-1)} = 32768, i.e.: x³²⁷⁶⁸ ą , ..., ą x - 1 f) Etc... II. Models a. Algebraic i. Light 1) Reflecting 2) Reflecting/Refracting ii. Male Honeybee Genealogy iii. Fibonacci's Rabbits b. Non-Euclidean Geometry III. The Special Traits of Golden Roots and Triangles a. Unit Modularity i. Ratio Approximations of Golden Roots: The Extended Quadratic (Golden) Euclidean Algorithm ii. Triangles Within Triangles b. Bisectors Forming Squares of Roots B. Music and its Application to Art Theory in General I. Chromatic Scales a. Equal Temperment i. Ratio Approximation b. Pure Temperment i. Pythagorean ii. Ptolemaic (Just Intonation; Present-day Method) iii. Polynometric II. Diatonic/Adiatonic Scales a. Major/Minor Keys C. Subliminal Art Forms

Anthropology Section

Theism Polysian style

TO BE CONTINUED..............