January 6, 2014 at 7:45 pm

Protected: Sacred Geometry Classes: Level 2 Class 1

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  • Cimmeron Munchie

    re: Lesson 1: Introduction to Proportion, Golden Section, Divine Symmetry
    WHOLE is to the Larger-PART :AS: the Larger-PART is to the Smaller-PART

    Really enjoyed the lesson Randall and the overhead format is also great.

  • Cimmeron Munchie

    re: Lesson 1: Introduction to Proportion, Golden Section, Divine Symmetry

    Randall, I searched your excellent copy of EUCLID’S ELEMENTS OF GEOMETRY
    The Greek text of J.L. Heiberg (1883–1885) for a basic definition of a Square Root, but I could not find one? Seems Euclid was very careful to state “the Square Root of an Area”.

    Also seems that Euclid was very careful to NOT state … what a Square Root is NOT.
    (dang … double negatives)

    I find that interesting because it seems that any other Math book: Modern Second Course in Algebra (1935) or Basic Technical Mathematics with Calculus (1964-1990) do not hesitate to state: “Every ‘NUMBER’ has 2 Square Roots.” ie: (+a, +a) and/or (-a, -a)

    My understanding is that even in 1935, the ‘Mathematics Moderns’ had already excised most of Geometry from Western academics. I suggest that this was to instill Linear thinking, en masse to the Masses.

    I bring this up because you drew a Square ‘form’ while you mentioned Quadratics and because once, I heard you mention your interest in GRIDS?

    Randall, I contend that in the ‘NUMBERS’ system as in GEOMETRY, there are in fact,

    4 Square Roots for each and every Square.

    it’s Numbers ( plural, dualities ) NOT Number ( singular, linear ).

    ergo: (+aX, +aY) and/or (-aX, -aY) and/or (+aX, -aY) and/or (-aX, +aY)

    There … I feel better now 🙂

    Just wondered if you’ve ever run across the same in the land of GRIDS?

    Cheers Randall

    p.s.
    Still loving the Lessons!