13 August 2024
St. Pontian 236 AD; Bl. Philip Monarriz & Comps. 1936 AD; St. Hippolytus 235 AD; St. Casian 3rd century AD; St. Radegund 587 AD
This article will be about some of the properties of the Multiplication/Division Tables and Transcendental Fibonacci Sequence. There is a way of breaking a Transcendental Fibonacci Sequence into an arithmetic formula and in that way obtaining all the terms of this sequence. To do this, I have to bring back certain properties of the Multiplication/Division Table. We started with two numbers:
P(ater) = (7/5)1/2 * π = 3.71718255693
And
F(ilius) = (5/7)1/2 * e = 2.29736745287
We can obtain the third essential, the parent number, by division of P/F:
S(piritus) = P / F = (7/5) * (π / e) = 1.61801828971
The classical Fibonacci Golden Ratio is good for rough calculations of the properties of bigger objects, architecture, nature's patterns, etc. However, the Transcendental Fibonacci formula is superior in accuracy.
Classical Fibonacci Golden Ratio:
Classical Fibonacci Golden Ratio = (51/2 + 1) / 2 = 1.61803398875
Now, to calculate more of these transcendental numbers upwards (not proven yet if they are transcendental indeed), we multiply factors of one pair to obtain the result, i.e., third pair; and to calculate transcendentals downwards, we divide two factors obtaining the third entry. In other words:
Transcendentals upwards:
STx = F * P
FTx = P * STx
PTx = STx * FTx
Etc.
Transcendentals downwards:
PVx = F / S
FVx = S / PVx
SVx = PVx / FVx
Etc.
Here is the link to the previous article with detailed calculations for ‘Constants going down’
>>> https://luxdeluce.com/357-145-division-multiplication-table-of-transcendental-constants-in-quantum-physics-and-cosmology.html
And detailed calculations for ‘Constants going up’
>>> https://luxdeluce.com/356-144-multiplication-division-table-of-transcendental-constants-in-quantum-physics-and-cosmology.html
To obtain the Transcendental Fibonacci Sequence using an arithmetical formula, we need one pair just below the entry S, i.e., FVx and PVx.
And the formula for the terms of Transcendental Fibonacci going up is:
Sn+1 = [(FVx)(n+1)] * [(PVx)n] Eqn. 1
Where
Sn+1 is the term of the Transcendental Fibonacci Sequence
FVx = 1.13955788072 (from the tables; see link above)
PVx = 1.41986494682 (from the tables; see link above)
n >= 0; n are the integers
You will see from the calculations that the ratio (‘golden ratio’) of two consecutive terms is equal to:
GR = 1.61801828971
Another important observation is that the terms of the Transcendental Fibonacci Sequence are exact values, they can be rounded up to the nearest integer as well, but only the first six terms are the same as in the case of the classical Fibonacci sequence, i.e., 1, 2, 3, 5, 8, 13; the next terms are slightly smaller than in classical Fibonacci sequence.
Here are the calculations of the first fifteen terms:
Sn+1 = [(FVx)(n+1)] * [(PVx)n] Eqn. 1
Where
Sn+1 is the term of the Transcendental Fibonacci Sequence
FVx = 1.13955788072 (from the tables; see link above)
PVx = 1.41986494682 (from the tables; see link above)
n >= 0; n are the integers
n=0; S0+1 = S1 = (1.13955788072)0+1 * (1.41986494682)0 = 1.13955788072 = approx. 1
n=1 S1+1 = S2 = (1.13955788072)1+1 * (1.41986494682)1 = 1.84382549318 = approx. 2
n=2 S2+1 = S3 = (1.13955788072)2+1 * (1.41986494682)2 = 2.983343371 = approx. 3
n=3 S3+1 = S4 = (1.13955788072)3+1 * (1.41986494682)3 = 4.82710413875 = approx. 5
n=4 S4+1 = S5 = (1.13955788072)4+1 * (1.41986494682)4 = 7.81034278281 = approx. 8
n=5 S5+1 = S6 = (1.13955788072)5+1 * (1.41986494682)5 = 12.6372774715 = approx. 13
n=6 S6+1 = S7 = (1.13955788072)6+1 * (1.41986494682)6 = 20.4473460809
n=7 S7+1 = S8 = (1.13955788072)7+1 * (1.41986494682)7 = 33.084179935
n=8 S8+1 = S9 = (1.13955788072)8+1 * (1.41986494682)8 = 53.5308082347
n=9 S9+1 = S10 = (1.13955788072)9+1 * (1.41986494682)9 = 86.6138267866
n=10 S10+1 = S11 = (1.13955788072)10+1 * (1.41986494682)10 = 140.142755882
n=11 S11+1 = S12 = (1.13955788072)11+1 * (1.41986494682)11 = 226.753542187
n=12 S12+1 = S13 = (1.13955788072)12+1 * (1.41986494682)12 = 366.891378515
n=13 S13+1 = S14 = (1.13955788072)13+1 * (1.41986494682)13 = 593.636960772
n=14 S14+1 = S15 = (1.13955788072)14+1 * (1.41986494682)14 = 960.515459976
The ratio (‘golden ratio’) of the two consecutive numbers is equal to
GR = 1.61801828971
Next, we shall discuss the Fractional Fibonacci Sequence and the complete Transcendental Fibonacci Sequence.
Miraculous picture of Our Lady of Absam, 17 January 1797 AD, St. Michael’s Basilica, Absam, Tyrol, Austria:
Schubert: Ave Maria - Elisabeth Kulman >>> https://www.youtube.com/watch?v=Rw9DueQot48
Comments powered by CComment