It seems that mathematical and physical constants can be derived by simple calculation of prime numbers and Fibanacci numbers.
In Fibonacci numbers series:
610/377 = 1.61803 = Golden ratio
In Prime numbers series:
11251/4139 = 2.71828 = Euler number
16063/5113 = 3.14159 = PI
33911/5081 = 6.67408 = constant of gravitation
51637/7793 = 6.62607 = Planck constant
11909/7433 = 1.60217 = elementary charge (Charge of electron)
532999/5851 = 9.109383 = electron mass
14593/1489 = 9.8005 = acceleration of gravity
13327/2213 = 6.02214 = Avogadro constant
2621/1567 = 1.67262 = Proton mass
Is there any implicit rule here?
Thinh
I could only understand this in the sense that you can obtain
the Euler constant from the harmonic series and ln
Value of irrational numbers cannot be exactly expressed in the form of fraction with integers.
Thinh,
I don't think there is a rule. Some connections ofcourse. An example:
The Riemann z-funktion gives pi*pi/6 for z(2) and it can also be written as a product over the primes. A proof is on wikipedia:
https://en.m.wikipedia.org/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function
Kind regards
Dear George, can you explain what you mean by density-type arguments? Thank you in advance.
definately not scientific constants
Mathematical constants maybe in the sense of Lena or mine
The concept is that any irrational number can be approached by
some adequate rational number within some prefixed small error.
ie. a rational number of the form p/q with large enough p and q
Or as stated by Peter, that the rationals can form a dense set.,there are an arbitrary large number in any small interal.
Some infinite series of rationals added together can sometimes be considered to give the irrational number, in Lenas example, if the series is convergent.
Ok, I guess that "density-type arguments" means that ratios of primes "form a dense set in the reals". Makes sense.
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