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The Pattern of Pi Through the Unification Construction

The Pattern of Pi

In the past, we have been unable to find the pattern in pi because of the anthropomorphic habits of mathematicians.  Because our brains are digital, they look for a digital pattern in pi.  Human brains are mathematical.  The real, physical universe is proportional.  Our mathematics and arithmetic digits are our detection of and sense of proportion.  There are electromagnetic waves, and our detection of them is our sense of sight, or vision.  There are vibration waves that travel through liquids, solids and gases, and our detection of them is our sense of sound, or hearing.  There is proportion in the universe, everywhere, in all things, and our detection of proportion is our sense of proportion, our mathematics.  Proportion is not the result of universal forces, but rather evolutionary proportion is the source of all material shapes in the real, physical world, in essence the most fundamental Force of Nature.

The pattern of pi is proportional, not digital.  We see the Fibonnaci series everywhere, the Golden Mean, the spiral form, in Nature.  We also see pi in Nature and our intuition tells us there should be a visible relationship, a pattern, of interaction between pi and phi.  What I have designated as Phi (1.618033988…), and phi (0.618033988…) is also labelled as theta .  Therefore, looking for a pattern of decimal digits in pi has not been successful.  The real pattern in pi is the transformation from pi as a straight line back to the value of the Golden Mean or Golden Section (1.618033988…).  We begin (viewing the Unification Construction in reverse) with pi:    3.1415926535897932384626433832795…  .

Beginning with pi, we then multiply pi by 1.118, and the result is:

3.5123005867133888406012353025065

We then divide by ten, and the result is:

0.35123005867133888406012353025065

This value is the difference between two values derived from trigonometry and the construction of the pentangle and pentagon.

0.35123005867133888406012353025065

equals .         (pi*V)^2         .   =  .         (3.1426968052735445528926416093549)^2_____.

(pi*E) * sqrt(cos 36)         (3.1418181818181818181818181818181) *sqrt(cos 36)

where sqrt(cos 36) = sqrt(0.80901699437494742410229341718282)

= 0.89945371997393363613061379181213

Therefore, =    9.8765432098765432098765432098766

2.8259200511181042240612738768206

equals:  3.4949832377489899930912943111988                  line, value A

then     (pi*V)^2    =  9.8765432098765432098765432098766

(pi*D)              3.1416407864998738178455042012388

equals:             3.1437531790132111258881742027519       line, value B

A minus B =    0.3512300587357788672031201084469

Or, times 10 = 34.949832377489899930912943111988

minus 31.437531790132111258881742027519

= 3.512300587357788672031201084469

Which is the same as:

(40/9)^2 * 0.5            =    9.8765432098765432098765432098765

(1.728/0.55)*sr(cos 36)           2.8259200511181042240612738768207

minus:  .        (40/9)^2 * 0.5

[(1.618033988)^2 * 1.2]

same as:           9.8765432098765432098765432098765

3.1416407864998738178455042012388

THEREFORE, the pattern of pi is through the relationship of pi and Phi:

pi =  3.1415926535897932384626433832795…

Phi =  1.6180339887498948482045868343656…     Theta, Fibonacci series, Golden Mean

Seeking the pattern in pi:

In order to reveal the pattern of pi we can pursue that goal by unraveling the process of the Unification Construction in reverse, our purpose being to disclose the relationship between pi and Phi, (1.618033989… and 3.141592653…)  Or, Phi^2:  2.618033989…

(40/9)^2 * 0.5       .   -   (40/9)^2 * 0.5    =   pi * 1.118

(1.728/0.55) * sr(cos36)         (Phi)^2 * 1.2                 10                   [ multiply by 0.55]

(40/9)^2 * 0.275   -   (40/9)^2 * 0.5    =   pi * 1.118                           [multiply by 10]

1.728 * sr(cos36)       (Phi)^2 * 1.2                 10

(40/9)^2 * 2.75   .   -   (40/9)^2 * 5 .    =   pi * 1.118

1.728 * sr(cos36)         (Phi)^2 * 1.2

Check; go back:

(40/9)^2 * 0.275   .   -   (40/9)^2 * 0.5    =   pi * 1.118

(1.728) * sr(cos36)         (Phi)^2 * 1.2                  10                          [ change 1.2 to (6/5)]

(40/9)^2 * 0.275  .   -   (40/9)^2 * 0.5 .    =   pi * 1.118

(1.728) * sr(cos36)         (Phi)^2 * (6/5)                  10                        [process 6/5)

(40/9)^2 * 0.275  .   -   (40/9)^2 * 2.5    =   pi * 1.118

(1.728) * sr(cos36)           (Phi)^2 * 6                   10              [get common denominator]

Rewritten with common denominator (omit right side of equation temporarily):

(40/9)^2 * 0.275  .   -   (40/9)^2 * 2.5           [process common denominator]

(1.728) * sr(cos36)           (Phi)^2 * 6

[ (Phi)^2 * 6 * (40/9)^2 * 0.275 ]  -  [ (40/9)^2 * 2.5 * (1.728) * sr(cos36)]

(1.728) * sr(cos36) * 6 * (Phi)^2

Then, continue the calculation, which will result in (pi * 1.118) divided by 10,

or:  3.5123005867133888406012353025065… / 10

same as:  0.35123005867133888406012353025065…

[Phi^2 * 32.592592592592592592592592592593]

minus [85.333333333333333333333333333333 * sr(cos 36)]

divided by:  [ 10.368 * sr(cos 36) * Phi^2]

OR:  (Key process here):  convert (40/9)^2 to (1600/81) and process that fraction/ratio:

1600 * [ (Phi^2 * 6 * 0.275) - (2.5 * 1.728 * sr(cos36) ]  .

81   * [6 * 1.728 * sr(cos 36) ] * Phi^2

IS:  1600 times:

[4.3197560814373264995375682767033 - 3.8856400702873933080842515806284]

same as 1600 times 0.43411601114993319145331669607491

which is:  694.58561783989310632530671371986    (numerator)

AND denominator is:  81 * [6 * 1.728 * sr(cos36)] * Phi^2

same as 81 * [9.3255361686897439394022037935081] * Phi^2

same as:  755.36842966386925909157850727416 * Phi^2

such that entire expression is the same as:

1    .    times             694.58561783989310632530671371986

Phi^2                           755.36842966386925909157850727416

equals       1   .            times  0.91953223164089099757046195519357

Phi^2

same as:           0.91953223164089099757046195519357

2.6180339887498948482045868343656

equals:   0.35123005873577886720312010844676

which IS our pi * 1.118 divided by 10      end thus far, except for another viewpoint:

Let X = numerator = 694.58561783989310632530671371986

Let Y = denominator = 755.36842966386925909157850727416

Equation rewritten:    __1        *   X    =    (pi * 1.118)

Phi^2         Y                 10

Equation processed:    __1        *    =    (pi * 1.118)          [multiply by 10]

Phi^2         Y                 10

__1        *  10 *X    =    (pi * 1.118)               [divide by 1.118]

Phi^2            Y

__1        *     10      *  X   =  pi                        and then, entering the numerical values:

Phi^2          1.118       Y

10       =  8.9445438282647584973166368515206

1.118

X  =  0.91953223164089099757046195519357                                [multiply]

Y

1      *  8.2247963474140518566230944113915   =  pi

Phi^2

8.2247963474140518566230944113915 =  3.1415926541661794919778185013127

2.6180339887498948482045868343656

The result divided by the "pi exactly" stored in this same calculator is:

1.000 000 000 1834694427543169076899  (precision to the 9th decimal place)

and the interesting number here is:  8.2247963474140518566230944113915

which, divided by 2 equals:  4.1123981737070259283115472056958

and divided by 2 again = 2.0561990868535129641557736028479

and the square root of (2 plus the square root of 5) is:

sqrt [4.2360679774997896964091736687313]

which equals:  2.0581710272714922503219810475805

And:    2.0561990868535129641557736028479

2.0581710272714922503219810475805

equals:  0.99904189671710932672171243316141  (my old number "Gh" ost)

the inverse of 1.0009590221251371319544933802193  (my old number "Ho" ly)

which takes us back to old work from years ago searching for the possibility of constructing the inverse of the factor of a "pi-line" and pi exactly.  (A = [pi * X]; therefore we want [1/X]. )

This work tells us we can construct 0.99904189671710932672171243316141

as a ratio in a triangle and then multiply that ratio times the constructed line length of an old

pi-line (specifically 4 times the square root of 0.618033988…)

3.1446055110296931442782343433718 * 0.99904189671710932672171243316141

= 3.1415926541661794919778185013127

pi exactly times:  1.000 000 0001834694427543169076899  (again precision to 9th place)

the pattern in pi with the "bug" of the limited precision of a desktop computer calculator.

The constructions for "Seeking the Pattern in pi" are possible and relatively easy:

Can we construct:

1600 * [ (Phi^2 * 6 * 0.275) - (2.5 * 1.728 * sr(cos36) ]  .

81   * [6 * 1.728 * sr(cos 36) ] * Phi^2

and/or:

X = 694.58561783989310632530671371986 = 0.91953223164089099757046195519357

Y      755.36842966386925909157850727416

Yes.  We need to divide and multiply to make the line lengths manageable, so that we can get to

6.9458561783989310632530671371986 = 0.91953223164089099757046195519357

7.5536842966386925909157850727416

For the numerator:

1600 * [ (Phi^2 * 6 * 0.275) - (2.5 * 1.728 * sr(cos36) ]

We see that if we divide by 100 we convert 1600 to 16, and divide by 2 to get 8.  (We have divided by 200).

For the denominator:

81   * [6 * 1.728 * sr(cos 36) ] * Phi^2

We see that 81 * 6 = 486.  Divided by 200 equals 2.43.  Or, 8.1 * 0.6 = 4.86, and that divided by 2 equals 2.43.  (We have divided by 200.)

8 * [ (Phi^2 * 6 * 0.275) - (2.5 * 1.728 * sr(cos36) ]  *    __1   .

2.43 * 1.728 * sr(cos 36) ]                                     Phi^2

numerator in (X/Y) equals:  8 times

[4.3197560814373264995375682767033 - 3.8856400702873933080842515806284 ]

same as 8 times [0.43411601114993319145331669607491]

equals:  3.4729280891994655316265335685993                  (numerator)

This constructed line value = 6.9458561783989310632530671371985 / 2

denominator in (X/Y) equals:  2.43 * 1.728, or 4.19904 times

sr(cos 36), same as times 0.89945371997393363613061379181213

which equals 3.7768421483193462954578925363708, and which equals

7.5536842966386925909157850727416 / 2

SO THAT our constructed ratio equals:

3.4729280891994655316265335685993

3.7768421483193462954578925363708

equals:  0.91953223164089099757046195519357

the correct result through constructions of manageable size.

This work should be sufficient evidence to support further exploration of the proposition that proportion is everything, because it demonstrates a proportional relationship between pi and the Golden Mean, or the sum of the Fibonacci series, so dramatically visible as a proportion in natural development.  What is suggested is that the Pythagorean statement "Proportion is everything" was a true statement about the real physical universe.  I believe that the fundamental force of proportion, including my viewpoint on "The Hiram Key" or the Self-reciprocal Construction (SOLITU H), enables molecular matter to measure itself and that this process of self-measurement is the necessary operation that precedes self-assembly.  This is the Secret of Life in the Universe.  Proportion is "The Force" that is the cause and shape of everything:  atoms, molecules, plasma, objects, forms of energy, organisms, ecosystems, planetary systems, galaxies, everything.  Our mathematics is our sense of proportion, and this sense of proportion varies from person to person.  And that is why we disagree over much and fight over everything.

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