1. Number Systems
Background: Number Systems is a post to explore number systems in general and for use in the
physical and computational sciences.
Post 8.2.1
Natural Events in Fibonacci Number Space
Energy Production
Posts 1 โ 8 have established:
1 ๐ท = (1 +
๐พโ
๐
๐๐ท
)
โ1
(1 +
๐พ ๐ท
๐
๐๐ท
)
+1
For natural events, this definition should correlate to the Bernoulli base of natural logarithms:
โซ
1
๐ฅ
๐๐ฅ
๐
1
= 1 where lim
๐โโ
(1 +
1
๐
)
๐
= ๐
A mathematical description of nature should not be accurate unless the number system complies
with both natural conditions of the number one shown above.
Natural examples:
1
๐3
2 =
1
35
2 ๐ฅ 10โ16
meter-2 sec+2
h = 6.6260700 E-34 = 6.6260700 x (1โ โ ๐ ๐ธ
๐{3}
) x 10-34
meter+2 kg+1 sec-1
๐๐๐๐๐ ๐ ๐ = ๐
when g = gEarthSurface <g units: acceleration+1 second+2>
It has been shown
๐ธ
๐ธ ๐ต
= ๐๐๐ต
To be rigorous, energy can be defined as a ratio:
๐ธ
๐ธ ๐ต
= ๐๐๐ต
Kilogram+1 Meter+3
2. Define
๐ธ
๐ธ ๐ต๐ท
=
(๐๐๐๐๐) ๐ท
๐
๐ฅ ๐ ๐ท
๐ ๐ท =
(1 โ ๐ ๐ธ
๐{๐ท}
)
๐ ๐ท
๐ท
๐ท+1๐ท
๐ ๐ = ๐ ๐ ๐ ๐ + ๐ ๐
And so on for D = F(n).
To be rigorous, the numerical value of hฮฝ should be the value hฮฝ = hฮฝ(r) while physical
results at spatial location r from a center of mass should be dimensionless.
๐ธ
๐ธ ๐ต
= ๐๐๐ต
Kilogram+1 Meter+3
Define
๐ธ ๐ต_๐ธ = ๐ธ ๐ต_๐ธ๐๐๐กโ๐ ๐ข๐๐๐๐๐
๐ธ ๐ต_๐บ๐๐ = ๐ธ ๐ต_๐ด ๐๐๐ ๐๐๐ก๐๐ก๐ข๐๐ ๐ด
๐ด ๐บ๐๐ = 35,786 ๐๐
Then
๐ ๐ท = ๐3
๐ธ = ๐ธ ๐ท3 = โ3 ๐
๐ธ ๐ท3_๐ธ
๐ธ ๐ต_๐ธ
= โ3 ๐ ๐ต_๐ธ
๐ธ ๐ท3_๐บ๐๐
๐ธ ๐ต_๐บ๐๐
= โ3 ๐ ๐ต_๐บ๐๐
๐ธ ๐ต_๐บ๐๐ < ๐ธ ๐ต_๐ธ
โ๐ ๐ต_๐ธ < โ๐ ๐ต_๐บ๐๐
Post 8.2.2 is intended to further clarify energy production in Fibonacci energy space.