FUNCTIONS OF THE ‘GOLDEN BOWL’ ARRANGEMENTS

ON THE Φ-LEVEL OF EXISTENCE ITSELF

Constant |
Symbol |
Value* |
Φ-Structure | Φ-Value | Difference (pph) |
---|---|---|---|---|---|

Speed of light in vacuum | c |
299792458 |
φ raised to the value of the
diameter of the six-pointed ‘defining bowl’ star (φ^{40.56}) at once the mean square megametric radius of Earth |
299368444 | 0.14 |

Triple-point temperature | Tt |
273.16 | fourfold perimeter of the pentagon enclosing the ‘defining bowl’ | 274.1640785 | 0.37 |

Permeability of vacuum | µ_{0} |
12.56637061 | circumference circumscribing the regular hexagon the side of which is the base of the ‘entry bowl’ | 12.56637061 | Exact |

Permittivity of vacuum 1/µ_{0}c^{2} |
_{0} |
8.854187817 | tenfold negative square root of the hundredth part of the circumference circumscribing the six-pointed ‘defining bowl’ star, at once of the ten-fold megametric diameter of Earth | 8.858998187 | 0.05 |

Gravitational constant | G |
6.67259 | square root of the ten-fold radius of the circle circumscribing the regular pentagon the side of which is the base of the ‘defining bowl’ | 6.673878524 | 0.019 |

Planck constant | h |
6.6260755 |
total length of x and y axis segments
intersected by the first four-quadrant sweep of the
φ-spiral the initial
bounds of which are the rectangle, 1 by φ |
6.626053279 | 0.00034 |

(h/2π) |
1.05457266 | inverse fourth root of COS 36, the central angle of the regular decagon embodying φ-proportionality | 1.054412604 | 0.015 | |

Elementary charge | e |
1.60217733 | φ | 1.618033989 | 0.99 |

Magnetic flux quantumh/2e |
F_{0} |
2.06783461 | cube of the hundredth part of the circumference circumscribing the six-pointed ‘defining bowl’ star, at once of the ten-thousandth part of the megametric diameter of Earth | 2.068675272 | 0.04 |

Electron mass | m_{e} |
9.1093897 | fourth root of the hundredfold perimeter of the pentagon enclosing the ‘defining bowl’ | 9.098873777 | 0.12 |

Proton mass | m_{p}_{
} |
1.6726231 | square root of the tenth part of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ | 1.672893261 | 0.016 |

Proton-electron mass ratio | m_{p}/m_{e} |
1836.152701 | the
φ-to-the-fourth power of
1/100,000,000th of φ raised to the value of the diameter of the six- pointed ‘defining
bowl’ star (≈ φ^{40.56}), at once to the mean
square megametric radius of Earth |
1836.388737 | 0.013 |

Neutron mass | m_{n} |
1.6749286 | square root of the tenth part of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ | 1.672893261 | 0.12 |

Compton wavelength h/m_{e}c |
_{c} |
2.42631058 | φ root of the area of the pentagonal triangle enclosing the ‘entry bowl’, outside the bowl | 2.42687961 | 0.024 |

/2π_{c} |
3.8615905 | φ root of the area of the pentagonal triangle enclosing the ‘entry bowl’, outside the bowl, divided by the hundredth part of the area of the circle circumscribing the pentagon | 3.893903367 | 0.84 | |

Compton wavelength of the proton |
,_{c}_{p} |
1.3214099 | ratio of the area of the circle to the area of the inscribed pentagon in the pentagonal arrangement of ‘golden bowls’ | 1.321306399 | 0.0078 |

_{p}/2π |
2.1030892 | ratio of the area of the circle to the area of the inscribed pentagon in the pentagonal arrangement of ‘golden bowls’, divided by the hundredth part of the area of the circle circumscribing the pentagon | 2.120022524 | 0.81 | |

Fine-structure constant m_{0}ce^{2} |
α | 7.29735308 | the hundredfold ratio of the axis segments to
the lengths from the origin to the sides of the rectangle in the sweep of the φ-spiral the initial bounds of which are the ‘golden rectangle’, 1 by φ, divided by twice the total length of the axis segments intersected in the first four-quadrant sweep |
7.294901726 | 0.03 |

Inverse fine-structure constant |
α^{-1} |
137.0359895 | square of
the diameter of the rim of the ‘defining bowl’ in
the pentagonal arrangement of ‘golden bowls’, at once the square of tenfold
the constant ratio of the
diameter of the base of a bowl to that of the rim of the next smaller in the infinite
pentagonal series of bowls, identically the square of tenfold
the ratio of the length of the
φ-spiral from the x-axis in the
fourth quadrant to -, to the length of the spiral through
the first four quadrants of the coordinate plane |
137.082039324 | 0.03 |

Rydberg constantm_{e}cα^{2}/2h |
R_{∞} |
10973731.534 | One billion times
φ^{-4} divided by twice the
total length of x and y axis segments intersected by the first
four-quadrant sweep of the φ-spiral the initial bounds of which are the rectangle, 1 by
φ |
11009422.02 | 0.33 |

Avogadro constant | N_{A}, L |
6.0221367 | Tenfold inverse of the square root of the
φ^{-1} section of the radius of the circle circumscribing the ‘entry bowl’
pentagon |
6.027198883 | 0.08 |

Faraday constantN_{A}e |
F |
96485.309 | the eighth power of the area of the pentagonal triangle enclosing the ‘entry bowl’, outside the bowl | 96420.4214 | 0.067 |

Molar volume of ideal gas at s.t.p. | V_{m} |
22.41383 | 100 times the inverse of the radius of the circle circumscribing the ‘entry bowl’ pentagon | 22.45139883 | 0.17 |

Molar gas constant | R |
8.314510 | one hundred thousand times the eighth power of COS 72, the central angle of the pentagonal arrangement of ‘golden bowls’ | 8.314936042 | 0.005 |

Boltzmann constant R/N_{A} |
k |
1.380658 | square of the ratio of the side of the inscribed pentagon to the circumscribed circle’s radius in the ‘golden bowl’ arrangement | 1.381966012 | 0.095 |

Stefan- Boltzmann constant (π ^{2}/60)k^{4}/^{3}c^{2} |
σ | 5.67051 | ratio of the axis segments to the lengths from
the origin to the sides of the rectangle in the sweep of the
f-spiral the initial bounds of which
are the ‘golden rectangle’, 1 by φ, divided by the length from the
origin to the top of the rectangle third smaller than ABCD, φ ^{-2 }/5^{1/2
} |
5.659325165 | 0.198 |

Atomic mass unit | u | 1.6605655 | square root of the
φ^{-1 }section of the radius of the circle circumscribing the ‘entry bowl’
pentagon |
1.659145516 | 0.086 |

Electron charge to mass ratio | e/m_{e
} |
1.7588047 | square of the ratio of the area of the circle to the area of the inscribed pentagon in the pentagonal arrangement of ‘golden bowls’ | 1.7458506 | 0.74 |

Josephson frequency- voltage ratio | 2e/h |
4.835939 | 20φ divided by the total length of x
and y axis segments intersected by the first four-quadrant sweep of the
φ-spiral the
initial bounds of which are the rectangle, 1 by φ |
4.88385445 | 0.99 |

Quantum of circulation | h/2m_{e} |
3.6369455 | eighth power of the ratio of the diameter of the circle to the side of the inscribed pentagon in the arrangement of ‘golden bowls’ | 3.647450829 | 0.29 |

h/m _{e} |
7.273891 | the hundredfold ratio of the axis segments to the lengths from the origin to the sides of the rectangle in the sweep of the φ-spiral the initial bounds of which are the ‘golden rectangle’, 1 by φ, divided by twice the total length of the axis segments intersected in the first four-quadrant sweep | 7.294901726 | 0.29 | |

Bohr radius | a_{0} |
5.2917706 | square root of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ | 5.290152988 | 0.03 |

Classical electron radius | r_{e
} |
2.8179380 | tenth part of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ | 2.798571864 | 0.69 |

Thomson cross section |
σ_{e} |
0.6652448 | tenth part of the circumference circumscribing
the pentagon enclosing the ‘entry bowl’, divided by
φ^{3} |
0.6606532 | 0.695 |

Bohr magneton | m_{B} |
9.274078 | eighth power of the ratio of the area of the circle to the area of the inscribed pentagon in the pentagonal arrangement of ‘golden bowls’ | 9.29026936 | 0.18 |

Electron magnetic moment | µ_{e} |
9.284832 | eighth power of the ratio of the area of the circle to the area of the inscribed pentagon in the pentagonal arrangement of ‘golden bowls’ | 9.29026936 | 0.059 |

Gyromagnetic ratio of protons in H_{2}O |
’_{p} |
267513010 | 100,000,000 times the ratio of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ to the square of the distance from the intersection of the base of the ‘entry bowl’ with the radius to the intersection of the circumference with the radius bisecting the bowl | 267239833 | 0.10 |

’_{p}/2π |
42576020 | 100,000,000 times the ratio of the circumference circumscribing the pentagon enclosing the ‘entry bowl’ to the square of the distance from the intersection of the base of the ‘entry bowl’ with the radius to the intersection of the circumference with the radius bisecting the bowl, divided by one-tenth the area of the circle | 42878372.3 | 0.71 | |

Proton magnetic moment in Bohr magnetons | µ_{p}/µ_{B } |
1.521032209 | fourth root of the side of the pentagon enclosing the ‘entry bowl’ | 1.512694818 | 0.55 |

Ratio of electron and proton magnetic moments | µ_{e}/µ_{p} |
658.2106880 | fourth power of the ratio of the height of the pentagonal section enclosing the ‘entry bowl’ to the base of the bowl, times the area of the circumscribed circle | 656.7499373 | 0.22 |

Proton magnetic moment | µ_{p} |
1.4106171 | square root of the ratio of the radius of the
circle circumscribing the pentagon enclosing the ‘entry bowl’ to the distance
from the center to the mid-point of the side of the pentagon, times
φ, at once 2^{1/2} |
1.414213562 | 0.255 |

Magnetic moment of protons in H_{2}O in nuclear
magnetons |
µ’_{p}/µ_{N } |
2.7927740 | tenth part of the circumference circumscribing the ‘entry bowl’ pentagon | 2.798571864 | 0.21 |

Nuclear magneton | µ_{N } |
5.050824 | square of the ratio of the area of the pentagonal section enclosing the ‘entry bowl’ to the portion of itself exterior to the ‘entry bowl’ | 5.050528019 | 0.0059 |

Ratio of muon and proton magnetic moments | µ_{µ}/µ_{p} |
3.1833402 | square root of the half-radius of the
six-pointed ‘defining bowl’ star, at once of the fourth part of the mean square
megametric radius of Earth, the power of φ equivalent to c |
3.184274175 | 0.029 |

Muon magnetic moment | µ_{µ} |
4.490474 | ten times the inverse of the ‘foundational distance’ separating the bases of the ‘defining’ and ‘entry’ bowls in the pentagonal arrangement of ‘golden bowls’ | 4.49027977 | 0.0043 |

Muon rest mass | m_{µ} |
1.883566 | fourth root of the circumference circumscribing the regular hexagon whose side is the base of the ‘entry bowl’ | 1.882792527 | 0.04 |

First radiation constant 2π hc^{2} |
c_{1
} |
3.741832 | in the pentagonal arrangement of ‘golden bowls’, ten times the ratio, to the circumscribed circumference, of the square of the distance from the intersection of the base of the ‘entry bowl’ with the radius to the intersection of the circumference with the radius bisecting the bowl | 3.74195714 | 0.003 |

Second radiation constanthc/k |
c_{2
} |
1.438786 | half the fourth root of the perimeter of the pentagon enclosing the ‘defining bowl’ | 1.438658264 | 0.0089 |

* The physical values in the table are the 1986 CODATA recommended values. For the most recent recommended values of the fundamental physical constants, cf. the 2006 CODATA Recommended Values of the Fundamental Physical Constants, available at http://physics.nist.gov/ constants. October 2008. |

**Note**

^{
1} See also, on this web,
Common Biophysical Variables as Combinations of Planck Length (*l*_{p}),
Planck Time (*t*_{p}) and Planck Mass (*m*_{p})
& the Equivalent Golden Section Factors.