1. The document discusses number systems, specifically exploring Fibonacci numbers and their relation to natural events and parallel processing algorithms. 2. Key equations are presented relating the Fibonacci definition to the Bernoulli base of natural logarithms and the Planck constant. 3. An example is given applying Fibonacci numbers to the fine structure constant and relating expressions for the Planck constant and energy.

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 8.3
Natural Events in Fibonacci Number Space
Parallel Processing Algorithms
Posts 1 – 8 have established:
1 𝐷 = (1 +
𝛾∞
𝑓
𝑇𝐷
)
−1
(1 +
𝛾 𝐷
𝑓
𝑇𝐷
)
+1
For natural events, this definition should correlate to the Bernoulli base of natural logarithms:
∫
1
𝑥
𝑑𝑥
𝑒
1
= 1 where lim
𝑛→∞
(1 +
1
𝑛
)
𝑛
= 𝑒
A mathematical description of nature should not be accurate unless the number system complies
with both natural conditions of the number one shown above. It has been shown:
6.6260700 E -34 = 6.6260700 x (1 − 𝑅 𝐸
3
1⁄
5
2⁄
) x 10 -34
From posts 2 and 3, we could also write:
6.6260700 E-34 = 6.6260700 x (1∞ − 𝑅 𝐸
𝑓{3}
) x 10-34
A natural example:
1
𝑐3
2 =
1
35
2 𝑥 10−16
meter-2 sec+2
For F(n) = 4 where D = 5:
15 = (1 +
𝛾∞
𝑓
𝑇5→13
)
−1
(1 +
𝛾5
𝑓
𝑇5→13
)
+1
∫
1
𝑥
𝑒3
1
𝑑𝑥 = 1 𝑤ℎ𝑒𝑟𝑒 lim
𝑛→∞
(1 +
1
𝑛
)
𝑛
= 𝑒3 = 𝑒
ℎ = ℎ3 = 𝑏3 𝐸 𝐵 𝑥 𝑘𝑎𝑝𝑝𝑎 𝑤ℎ𝑒𝑟𝑒 𝐸 = (𝑚𝑎 𝑔)𝑥𝑏3

2. h = 6.6260700 E-34 = 6.6260700 x (1∞ − 𝑅 𝐸
𝑓{3}
) x 10-34
meter+2 kg+1 sec-1
𝒘𝒉𝒆𝒓𝒆 𝒂 𝒈 = 𝒈
when g = gEarthSurface <g units: acceleration+1 second+2>
Define
𝐸 𝐵 =
𝐸
𝑚
𝑥
1
𝑏_3
3
𝐸
𝐸 𝐵
= 𝑚𝑏_3
3
𝐸
𝐸 𝐵
= 𝑚𝑉3
𝐸
𝐸 𝐵
= 𝑚𝑉𝐵
To be rigorous, the numerical value of hν should be the value hν = hν(r) while physical results at
spatial location r from a center of mass should be dimensionless.
The arithmetic statement
1 𝐷 = (1 +
𝛾∞
𝑓
𝑇𝐷
)
−1
(1 +
𝛾 𝐷
𝑓
𝑇𝐷
)
+1
1
𝑐3
2 =
1
35
2 𝑥 10−16
𝑏3 =
1∞
35
2 𝐸 − (8+1
𝑥 2+1
)
𝑏3 =
1∞
𝑐𝐷+_1𝐷
𝐷−_1𝐷
Post 8.3.1 is intended to further clarify parallel processing through algorithms using Fibonacci
Number Space.