Big Bang, Hydrogen, Phi, Fibonacci Series, Creation, God,

Pentagon and the Bishop’s Mitre

© 2009 by Michael Joyce

The proportion 1/ √f is contained at the heart of the hydrogen molecule, the very same relationship that exists between the height and half the length of the base of Giza’s Great pyramid.

Why is it that Bishops wear a mitre, shaped like the pentagon, a shape linked to occult practice.

The pentagon is also present in the geometry of the hydrogen molecule.

Hydrogen atoms manifested from a singularity, according to the Big Bang Theory.

These eventually coalesced to form suns or stars, in which nuclear reactions convert hydrogen into heavier atoms like carbon, oxygen and iron for example. The different atoms of the chemical elements are the building blocks of our environment.

Everything we perceive is made of atoms.

The perimeter, 2701, of this vesica piscis has Biblical significance.

The Hebrew gematria of the first 7 words of the book of Genesis ( translation: "In the beginning God created the Heavens and the Earth" ) is also 2701.

SEVEN words and NUMBER 2701 ( 37 x 73 )

This correspondence is amazing, since the manifestation/creation of hydrogen was essential to the formation/creation of planet Earth via the new elements produced by the nuclear reactions taking place in all suns/stars.

2701 is a special number because it is equal to 73 x 37 ( reflected numbers ). 3 & 7 relate to the 3 primary/ trinity and 7 spectrum/perfection rays of ( sun / spiritual? ) LIGHT.

What does the Bishop’s mitre symbolize? Is there any significance at an unconscious level?

The diagram ( not to scale ) shows two bonded hydrogen atoms, which contain a pentagram ABCDE. Calculations. Assumptions: OX= O'X= 165.5 (covalent radius) OA = ON = 537 (atomic radius) O’F = 537 OF = O’G = 206 (O'F - OO') NB = 1405 {2(NF+OF+OX)} FG = 743 (OF+OO'+O'G) MG = MO’ = 103 ( O’G / 2 ) NF = 331 (ON- OF) GB = NF = 331 XB = 702.5 (XO'+O'G+GB) MB = 434 (MG+GB) EH = 537 {2(XO'+O'M)}   AC AC = 1021.7216 [2√(OA2 - OX2)] Pythagorus   AB AB = 868.61096 AX = AC/2 √(AX2 + XB2)   ED ED = 631.213 ED = 2EF = 2MH MH = MBtana tana = half AC/XB = 510.8608/702.5 a = tan-1 0.727203985 or 36.02479724 degrees   EA EA = 331.9887 Angle BAX = 90 - a AH = EA = half EH /sin(90-a )

O & O’ are the centres of each atom. NG & BF represent atomic diameter 1074. OX & O’X is covalent radius 165.5 ( half of 331 ) The lengths of the sides constituting the pentagon are AB = BC = 868.611 CD = AE = 331.9886 DE = 631.2131 Height of vesica piscis, AC = 1021.7216 Of particular interest:  AC / DE = 1.618 (36) EH / AE(or AH) = 1.617 (525) NB / AB = 1.618( 46) Because each approximate closely to the 1.618, the mathematical constant phi, symbol f . BX / XY & AB / AE approximate closely to 1 + f or f 2. (within 99.9/8% accuracy) phi has significance as a 'growth' constant in Nature.  And hydrogen was the progenitor of atoms of all the other 100+ different chemical elements, after the Big Bang.   The fact that Phi is contained in could 'explain' the nuclear reactions in suns, in which H 'grows' / is converted to heavier atoms.   The presence of phi implies that it is inclusive in the 'Design' of the hydrogen molecule.   This requires a 'Designer'.   Indications of an 'Intelligent Designer', known as God, One, Creator etc.   Or is phi there just by chance?   Noticeably, EA is very close to 332 or covalent 'diameter' of hydrogen + 1 (ONE ) Link between Hydrogen & 'God'.   The divine numbers of hydrogen and our sun indicate that Hydrogen was 'designed' to be the stuff of suns/stars.   Because each value reduces to 3. H = 1074 reduces to 12 (1+0+7+4) then to 3. Our sun = 12 reduces to 3, ( 1 + 2 = 3 ). THREE : Trinity, Primary 3 like in white light

Pentagon ( mitre ) dimensions AB = BC = 868.61 CD AE = 331.9886 DE = 631.312 Reduced in proportion such that AE = CD = 1 (dividing each by 331.9886). Then AB = BC = 2.6164 DE = 1.901  whilst 537 / 31.9886 =1.6175

Perimeter of the pentagon (mitre) = AB + BC + CD + DE + AE = 9.1338 = 5 f + 1 ( 0.5% error ).

 1, 5 ( pentagon ) and phi.

Also noticeable is that the atomic radius of hydrogen divided by its covalent one approximates very closely to phi:

537 / 331 = 1.622

537 / 331.9886 = 1.6175

The earlier diagram of the hydrogen molecule has been modified to include rectangular figures ( or rhombus, where its 4 sides of equal length, opposite sides parallel ) This looks very much like an EYE.

Outer rhombus ABCN side 868.61, and inner rhombus shown in blue. ZM = 414.3667 ZM + √{ half EH )2 + ( half ED )2 } The perimeter of ABCN = 4 x 868.61 = 3747 (.44). 3747 contains numbers associated with (sun)Light, where the 7 spectral rays in light consist of 4 subsidiary rays ( yellow, orange, indigo, violet ) as well as the primary three. Uncanny since this rhombus, like the eye is associated with LIGHT.

Perimeter of the Inner rhombus 4 x 414.3667 = 1657.4668…… nothing obvious here.

The perimeters: ( length of CD 331.9886 approximates closely to covalent diameter of hydrogen, 331 plus 1 ).

Using this as a factor:

1657.4668 = 331.9886 x 4.9925

3747.44 = 331.9886 x 10.4655

This manipulation reveals other instances of phi.

(2 f - 1) 2 = 4.9997 ( cf. 4.9925 )each closely approximate to 5.

4 + 4 f = 10.472 ( cf. 10.4655 )

Evolution of (2 f - 1 ) and (2 f - 1 )2 The replication of 1, the ‘Start’ produces 2 ( like Father/Son). Combination of the 2 with1 produces 3 ( Trinity) followed by 4. If these reproductions are represented by triangles ( vectors ) as shown, then additional numbers h1 & h2 have association.  Using Pythagoras’ theorem :  h1 = √ ( 1 + 4 ), h2 = √( 9 + 16 ) h1 = √ 5 h2 = √25 = 5   Thus h1 = (2 f - 1 ) h2 = (2 f - 1 )2

The start of ‘Growth’ and its continuation involves phi, Nature’s growth constant.

Now 3 + 4 = 7.

SEVEN, the spectrum rays in sunlight ( 7 colours of the rainbow ).

SEVEN, the Biblical number of Perfection.

Diagram shows the pentagon, ABCDE, contained in the hydrogen molecule.

The joining of BE, EC, CA, AD, DB produces a 5-pointed star, in which a further pentagon, JKLMN, manifests.

BX = 702.5 BY = 971 AC = 1021.722 ED = 631.213 XY = 268.5 ( 103 + 165.5 ) EA = 331.9886 angle ABC = 72.04959448 angle BAC = angle CAE = c   Calculations JK = 456.6706162 AJ = 282.5254849 AJ = (AC – JK) / 2   tan b = ED/2 / BY b = 18.0058441 degrees tan b = JX / BX JX = 228.3353081 JK = 2JX   angle b = 18.0058441 degrees (tan-1 halfJK/BX) angle a = 18.01895277 degrees (36.02479687 – b) angle c = 53.97520313 degrees (90 – 36.02479687) angle d = 71.9941559 degrees (90 - b) angle AJE = d angle e = 108.0058441 degrees (180 – d) angle f = 54.03064097 degrees (180 – 2c – a) angle AED = angle CDE = f + d angle CAD = 17.99777045 degrees (c – i) angle ADE = 35.97743268 degrees (cos-1 x/AE) angle ANJ = 90.00807362 degrees (180 – d – angle CAD)   JN = 87.29472129 JN/sinCAD = AJ/sinANJ   angle h = 17.99777055 h = 180 – d – f - i angle m = 90.00807262 180 – h – d    EL = 600.2993927 EL/sin d = ED/sin m EM = 331.8441439 cos h = half ED / EM   ML = MN =268.4552488 ML = EL – EM     Perimeter JKLMN = 1168.170556 (JK + 2xLM + 2xJN)   1168.170556 = 331.9886 (earlier factor) x 3.518707 3.518707 = 2 f+√f- 1 (3.50801)   1168.17 approximates closely to 1170 (LIGHT numbers). { 11 / 7 is pi / 2 }

The lengths of its sides evaluate to: JK = 456.671 KL = JN = 87.29472129 LM = MN = 268.4552488 To calculate AD & angles i & ADE AD2 = AE2+ ED2– 2 x AE x ED x cos(f + d) AD = √755,140.3761 AD = 868.9881335   h2 = x2 + AE2 h2= (AD – x )2 + ED2 therefore (AD – x)2 + ED2 = x2+ AE2 solving : x = 268.6612583 angle i = cos x-1 / AE i = 35.97743265 degrees angle CAD = 17.99777045 degrees (c – i) angle ADE = 35.97743268 degrees (cos-1 x/AE) angle ANJ = 90.00807362 degrees (180 – d – angle CAD)   JN = 87.29472129 JN/sinCAD = AJ/sinANJ   angle h = 17.99777055 h = 180 – d – f - i angle m = 90.00807262 180 – h – d    EL = 600.2993927 EL/sin d = ED/sin m EM = 331.8441439 cos h = half ED / EM   ML = MN =268.4552488 ML = EL – EM

Comparison of perimeters of the outer & inner pentagons

Perimeter ABCDE = 2 x ( 868.611 + 331.9886 ) + 631.213 = 3032.4

Perimeter JKLMN = 2 x (268.4552488 + 87.29472129) + 456.671 = 1168.170556

ABCDE / JKLMN = 2.59585 = f+1 ( 99.15% accuracy )

Given JK = 456.6706162 JN = KL = 87.29472129 MN = LM = 268.4552488 angle NJK = 108.0058441 centre of circles ( not shown ) = C & C'   Calculations circle diameter = 868.5 angle NJY = 18.0058441 degrees (108.0058441 – 90) sin 18.0058441 = NZ / NJ NZ = 26.98402042 NL = 2 x NZ + JK = 510.638657 sin a = half NL / MN a = NJY = 18.005844 degrees cos a = half MN / CN where CN CN = 434.2532685 2CN = diameter = 868.5065   outer rhombus = 1073.820995 perimeter of outer rhombus = 4 x MN 3.234511652 x 331.9886   inner rhombus = 917 perimeter of inner rhombus = 4 x ZX ZX2 = (half JY)2 + (half JK)2 tan 18.0058441 = NZ / half JY half JY = 83.0194621 ZX = √59,29.24393 = 242.9593463 4ZX = 971.837385 = 331.9886 x 2.927321556   rhombus NX x 4 NX2 = (half JY)2 + (half NL)2 NX = √65,618.72369 = 256.1615188 4NX = 1024.646075 = 3.086389337 x 331.9886

Another diagram, not to scale, can be constructed, like an EYE as above, containing the pentagon JKLMN, within the mitre. Calculating the perimeter of the outer and inner rhombuses, and the diameter of the circles: Outer rhombus = 1073.820995 Inner rhombus = 1021.87916 Diameter of each circle 868.57   2.927321556 approximates closely to 3 ( 97.58% accuracy ).   3.234511652 approximates to 2f ( 99.95% accuracy ).

The diagram shows the two inner pentagons, JKLMN and J’K’LMN and the circle which will circumscribe them inside the hydrogen molecule. A circular ‘inner eye’ contains a hexagon. The diameter of this circle is NL, calculated earlier to 510.638657. Circumference of circle = 1604.218653 ( pi x diameter ) Perimeter of hexagon J’NJKLK’ = 1262.520118 ( 4 x NJ + 2 x JK ) ( 4 x 87.29472129 + 2 x 456.6706162 )

circumference of circle / perimeter of hexagon = 1.270647993, which approximates closely to

√f or { 1  /  ¹/_√f }

( 99.89% accuracy ).

Diagram showing triangular relationships between 1, 1 / √f , f , and 1 / √f.

The ratio of half base to height of the Giza’s Great pyramid, 484/380 or 1.2737, is also 1  /  ¹/_√f .

 Returning to the diagram, the distance MM’, between the vertices of the two pentagons within the mitre, evaluates to 165.8946787

MN² = (half NL)² + (half MM’)²

MN² - (half NL)² = (MN)²

MM’ = 2 x √{(half 510.638657)² - (268.4552488 )² }

MM’ = 2 x √6,880.261103 =165.8946787

The perimeter of a smaller inner circle, diameter MM’, is 521.1735038. ( pi x MM’ )

Significant ratios seem to be:

Diameters of outer / inner circles is 1.9 (018) 1.9 = 13 x 0.7, or 13 x 07 ignoring decimal point.

An association between 0, 1, 3 and 7,

LIKE: the invisible (0) sunlight (1) which consists of (3) primary rays (red, blue, green) within its (7) spectral ones – “Let there be Light.”

Notice that 1 /73 = 137 ( 13698 ), a significant relationship involving light numbers 1, 3, 7 , 0. Circumferences of hydrogen molecule ( excluding vesica piscis ) / inner circle = 7765, which closely approximates to 777 ( 4047.1412 / 521.1735038 ).

Or : ‘OUTER hydrogen perimeter is 777 times its INNER eye’.

777 = 21 x 37 (LIGHT)

3 x 7 = 21 ( present above ).

SEVEN – a number of LIGHT, the number (reduced) of every ATOM, number of PERFECTION. Hydrogen’s covalent divine number 331 reduces to 7 ( 3+3+1).

Other diatomic molecules.

Oxygen, Chlorine and Nitrogen molecules are diatomic because they each contain two covalently joined atoms like Hydrogen.

Divine numbers

Oxygen : covalent diameter 655, atomic diameter 1253

Nitrogen : 664, 1342.5

Chlorine : 880, 1611

In each case the perimeters of their mitres contained values of phi :

O = 5f+2; N = 5f+(2f - 1)2 ; Cl = 4f+2

Calculations to obtain the ratio of perimeter of hexagon / circumference of circle gave 0.861225558, an ABSENCE of the 1 / √f proportion.

SUMMARY

1- The universe exists because hydrogen manifested after the ‘Big Bang’.

2- Hydrogen coalesced to produce suns/stars, in which nuclear reactions convert hydrogen into

    atoms of heavier chemical elements, the building blocks of planets and life.

3- Nature’s ‘growth’ constant is 1.618 or phi, symbol f.

4- The vesica piscis of hydrogen has a perimeter of 2701 ( 6.037275nm ).

    2701 = 73 x 37, a pair of mirrored numbers, containing Light numbers 3 & 7.

   The Hebrew gematria for verse 1 in Genesis 'In the beginning God created the heaven and the

   earth': is 2701.

   The third verse : 'And God said, Let there be light: and there was light': numbers 3& 7.

5- The main mitres, which can be constructed in molecules of diatomic elements like hydrogen,

    have perimeters involving phi.

6- The value 1 + f ( BX / XY in the mitre ) seems unique to hydrogen ( absent in other diatomic

    molecules tested ).

7- The ‘eye’ consisting of inner and outer rhombuses contain values of 3 and 2f seems unique to

    hydrogen…. LIGHT & GROWTH.

8- The ratio 1 : 1 / √f seems unique to hydrogen’s ‘inner eye’ comprising of a hexagon enclosed

    by a circle… GROWTH

9- Tangent of the tip of hydrogen’s mitre ( 0.727203985 ) contains the solar factor 72, which can be

    used to convert measurements of planets, sun, moon, atoms etc into divine numbers.

Note on Phi & the Fibonacci Series

The Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 …………………. Numbers in this sequence can be represented by squares. Starting with two like ones at the centre (1, 1), a square of side ‘2’ can be added and so on, as shown.   When the squares are connected by one of their corners, a spiral is the result.   Any next number in the endless sequence is found by adding together the two previous ones. The next number will be 610 ( 233 + 377 ). By dividing a number in the sequence by its previous one, the value of phi (1.618) eventually reveals itself at the 13th member ( 233 / 144 = 1.618055.. ) 377 / 233 = 1.618025751…. 610 / 377 = 1.618037135…… This series gives us the value of phi, as 1.618, though in reality it an irrational number. Nature uses the Fibonacci series and phi in growth processes ( ammonites for example ).

'STRANGE' FACTOR

If we multiply the solar factor 72, by the Earth’s diameter 7920 (miles) the result is ‘57024’.

Let F = 57024.

The lengths of EA and ED in the mitre pentagon of the hydrogen molecule yield fascinating results: EA 331.9886 / F = 58(2191)

331 / F = 58(04574)

ED 631.213 / F = 11 (06925)

631 / F = 11(0655)

11 and 58 are the divine numbers of planets Earth & Mars

( material & spiritual? planes of existence).

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Created 17 March 2009