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 7
Natural Events in Fibonacci Number Space
EB
Posts 1 – 6 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>
𝐸 𝐵 =
𝐸
𝑚
𝑥
1
𝑏3
3
𝐸
𝐸 𝐵
= 𝑚𝑏3
3
Define
𝐸
𝐸 𝐵
= 𝑚𝑉3
𝐸
𝐸 𝐵
= 𝑚𝑉𝐵
Then the dimensionless ratio for energy equals mass x volume of space.
But we have used units defining Earth surface observation ag = g where radius = r Earth.
Then to be rigorous, for the observed constant h:
𝑎 𝑔 = 𝑔 𝑟𝐸𝑎𝑟𝑡ℎ
But this is not indicated in general number space F(n).
Fibonacci number space derives:
𝒂 𝒈 = 𝒈 𝒓
Where r is a radius from a center of mass in space. From mathematical rigor, r should represent
any radius from any center of mass.
To be rigorous, the numerical value of h should be the value h = h(r) while physical results at
spatial location r should be dimensionless.
Post 8 is intended to further clarify nomenclature through natural examples of Fibonacci Number
Space beginning from the value F(n) = D = 3.