Subject Outline
0. Introduction1. 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 (4th 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. xdegree: 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) 1st Degree = 2(2^0-1) = 1, i.e.: x1 - 1 b) 2nd Degree = 2(2^1-1) = 2, i.e.: x2 ± x - 1 c) 8th Degree = 2(2^2-1) = 8, i.e.: x8 ± x7 - 7x6
6x5 - 15x4 ± 10x3 - 10x2
4x - 1 d) 128th Degree = 2(2^3-1) = 128, i.e.: x128 ± , ..., ± x - 1 e) 32,768th Degree = 2(2^4-1) = 32768, i.e.: x32768 ± , ..., ± 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
Theism Polysian style