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Correction to π (how to measure a circle).

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    started a topic Correction to π (how to measure a circle).

    Correction to π (how to measure a circle).

    Greetings,

    π is one of the most integral relationships in existence: a line (diameter) to a curve (circumference).
    For over 2000 years, humanity has been "approximating" the circumference of a circle using the old
    ' method of exhaustion ' entailing the use of multiple straight-edge polygons. This has lead to the
    catastrophic " belief " that π is " transcendental ". The "approximated" number 3.14159... is indeed
    " transcendental " however this number is not the correct value of π as it becomes deficient at
    the thousandth decimal place viz. 3.14159... the correct value is 3.144605511029693144...

    What follows is a precise measure of π which shows how/why π is derived by way of Φ, the golden ratio.
    Note that Φ can be written in terms of π:

    (π+π√5) / 2π = Φ
    (3π+π√5) / 2π = Φ˛ = (Φ + 1)
    _______________________
    Difference: 2π and/or '1'
    If it is possible to write Φ in terms of π,
    is it also possible to write π in terms of Φ?
    The answer is yes.

    First and foremost, begin with a unit square s = 1 and inscribe a 2r = 1 circle (a circle whose radius is 1/2).
    Note that this 2r = 1 circle "kisses" the unit square four times equidistantly (π must be in some relation to '4').
    Where does the 2r = 1 circle itself come from as a natural consequence? It comes from the golden ratio:

    πbywayofΦishax600.jpg
    __________________________________________________ _______________________________
    AB = 1 (in relation to the unit square and/or the 2r = 1 circle)
    BC = √5 (the diagonal of a 2x1 double unit square)
    AC = (1 + √5)
    D = (1 + √5)/2 (Φ, incessantly coincides with the circumference of the 2r = 1 circle)

    As the graphic implies, if/when AC is rotated about the origin (the center of the square and/or 2r = 1 circle),
    point D incessantly coincides with the circumference of the 2r = 1 circle while "kissing" the unit square 4 times
    equidistantly (!). As such, π can be measured precisely, without the need for any approximation, by way of
    the golden ratio, expressed as a ratio of Φ. This ratio is precisely 4/√Φ and can also be expressed as
    √(8√5-8) and/or √(-8+8√5), an "octave" within which energy (frequency/vibration) may express itself.

    Understanding the union of Φ and π is thus understanding the union of line and curve viz. space and time.
    The nature of the relation between line and curve (implied: space and time) is (significantly) that of reciprocity (!):

    πbywayofΦquartercircle.jpg

    In the above image, DE has two relations: line and curve. The line is attained by multiplying Φ by √2/2
    (which is equivalent to taking the square root of Φ) viz. √Φ and/or Φ1/2. This operation simultaneously
    creates the four equidistant points relating the circle to the square (!). The corresponding curve may
    thus be found by taking the reciprocal of the line element viz. 2/√(2(1+√5)), giving us an exact measure
    of the length of one quarter circle (as a ratio) equal to π/4. By removing the base of '4' such to
    make a full circle, the expression becomes mechanically -√2(1+√5) + √10(1+√5) or simplified: √(8√5-8).
    This rational/irrational "octave" relation, like π itself, is scalar: it is a fixed constant and never changes.
    This "scalar" nature in/of π is owing to the unique property(s) of the (now re-related) golden ratio Φ:

    Reciprocal of Φ = 1/Φ = (Φ - 1), a natural "bridge" between multiplication and subtraction operations.
    Multiplicative of Φ = Φ˛ = (Φ + 1), a natural "bridge" between division and addition operations.
    Φ is the only irrational number which, if/when squared, produces itself back in addition to a rational '1'.
    __________________________________________________ _______________________________
    Φ is a naturally-occurring and universal (unique) constant/ratio whence π is ultimately derived.

    The nature of the relation between space (s) and time (t) is thus of reciprocity wherein any motion(s)
    can be measured as a velocity (v):

    s / t = v (speed) = physical
    t / s = e (energy) = metaphysical
    s / t x t / s = (unity) = light (datum) = 1

    √1 = +1, -1
    √+1 = 1 (real, rational and terminating numbers, static)
    √-1 = i (imaginary, irrational and non-terminating numbers, recursive)
    -(-1) = not (not unity) = unity
    Here is a website which provides a number of geometric proofs, as well as a real physical measurement
    of a real circle such that shows π ≠ 3.14159... but is rather 4/√Φ. Because the latter is a root of the function:

    Number Axesbef.jpg

    This single long-standing π blunder is truly the principle barrier of all planetary science(s), the measure of it
    being of the ignorance this humanity suffers (non-derogatory, non-rhetorical) esp. in light of what the correction
    to π clarifies as ultimately underlying e = MC˛:

    π ≠ 3.14159... (human approximation error)
    π = 4/√Φ
    π˛ = 16/Φ
    e = MC˛
    16 = Φπ˛ <-*rationally precedes Einstein's e = MC˛
    1 = Φπ˛/16
    ∞ = Φ(π/4)˛
    __________________________________________________ ___
    wherein:
    Φ = 1D "electric" (mass) constant (universal)
    π˛ = 2D "magnetic" (velocity) constant (universal)
    16 = " sweet 16 "
    1 = unity

    e = MC˛ was recently solved for on 04/13/2020 as a product of the ongoing scientific inquiry " whence human suffering? ".
    The catastrophic "approximation" of π is found (by the same) to be largely responsible for the dark ages of humanity
    (thus all sufferings associated) for not knowing the nature of the relationship between space (yang) and time (yin).
    This is presently reflected in/as humanity not knowing how to properly (precisely) measure a circle, as reciprocity
    is certainly a natural consequence of ordinary mathematics, and so of the relation between line and curve,
    and so of space and time, as space and time are merely multiplicative reciprocal aspects of (abstract) motion.
    There is nothing but motion (s / t) and the energy (t / s) constituency(s) behind that motion, thus space and time
    are never severed if/when in reciprocal relation.

    To close: Prof. Eric Dollard is certainly not far off with his 4-quadrant representation of electricity: indeed the '4'
    is intrinsic to the relation between a circle (curves) and square (lines) thus time and space. What is being missed
    by our present-day humanity is the importance of the nature of the relation between the two: reciprocity.
    The correction to π, along with the recognition of the reciprocal nature of (the aspects of) space and time
    are practically imperative at this point in time, as their reunion would naturally instigate a calibration
    which would equate to a significant rise/increase is human consciousness on the planet.
    Last edited by Ananalyst; 08-24-2020, 03:40 AM.
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