Miscellaneous Background Math quotation page: (ecclesiastes quote) Logic Logic Flow Logic Base Prime Factorial of Bases Base Two Logic The Logical Structuring of Mathematical Functions Dividing by The Unknowable Base Six Logic Imaginary Numbers Primes Unpredictable Occurence The Sahasrara Primes Their Predictability Polynomials in One and Multiple Unknowns Formation and Identity Complete Solutions Averaging Methods Plotting the Error of a Function: Best Fit (Newton) Partial (Approximate) Solutions Isolation of Terms Continued Coefficients Substitution Looping Formula (Serial) Polynometric Progression Continued Radicals Continued Fractions Ratios ?Incremental Progression Euclidean Algorithms Polynomial Derivation (Golden) Extention of the Quadratic Cubic Polynomial Transformation Long Version Short Version Quartic and Beyond Numeric Square Roots of Numbers (source for formula?) Suppression of Partial Quotients Approximation of Arctangent(1), or one-fourth pi The source Derivation to: Gauss's version---no suppression of any partial quotients Suppression of the First Partial Quotient, the "x^1" Coefficient Accuracy Testing ?Mixed?---Roots of Numbers The Partial Solution of: a*x^degree - b*x^0 = 0, Resulting in: x^(1/degree) = a/b Newton's Averaging of Partial Solutions Coefficient Methods "x^0": Pseudo-Geometric Progression "x^degree": Summation of Powers of Quadratic Roots Fibonacci Lucas Aesthetic Mathematics (some of it, anyway) The Golden Class Regular Polygons Chords Isosceles Triangles Roots of Golden Polynomials The Sacred Class Ratio Hybrids of Golden Roots Geometry Special Case: the Octagon All Others... Odd-Sided Polygons: Golden Beauty Golden beautifull polynomials are largely irreducible Even-Sided Polygons: Semi-Golden Power Reducibility of Semi-Golden Polynomials Models Algebraic Light Reflection Reflection/Refraction Male Honeybee Genealogy Fibonacci Rabbit Breeding Non-Euclidean Geometry The Special Traits of Golden Roots and Triangles Unit Modularity Ratio Approximations of Golden Roots: The Extended Quadratic (Golden) Euclidean Algorithm Triangles within Triangles Bisectors Forming Squares of Roots Music Theory Chromatic Scales Equal Temperment Ratio Approximation Pure Temperment Pythagorian Ptolemaic (Just Intonation, Modern) Polynometric Diatonic/Adiatonic Scales Major/Minor Keys Subliminal Art