Talking about Golden ratio, Euler's constant and natural logarithm, there is also another math constant. Call it Alisabana's constant... On July 24, 2015, Hilman P. Alisabana wrote on his blog (link: https://matematiku.wordpress.com/2015/07/24/prime-in-golden-tree/ ) about the prime number of the form 10^2k - 10^k - 1, where k = 253. On his blog, July 19, 2015, he also showed that the decimal expansion of the form 1/(10^2k - 10^k - 1) follows Fibonacci sequence, with the predictable decimal constant of digit number k. ( Link : https://matematiku.wordpress.com/2015/07/19/golden-ratio/ ) More generally, if x on the quadratic equations x^2 - x - 1 = 0 is replaced by u^k then the real solution of k is simply k = ln(phi) / ln(u), where ln is natural logarithm, and phi is golden ratio. If u = e (Euler's constant) then k = ln(phi) = 0.48121182... That's the Alisabana's constant. The ln(phi) arises in Hyperbolic functions as inverse hyperbolic cosecant of 2, or inverse hyperbolic sine of 1/2, so that the problem of the Hyperbolic equations e^k - e^-k = 1 or e^2k - e^k - 1 = 0 have the real solution k = ln(phi) or e^k = phi, where e is Euler's constant and phi is golden ratio. (Link : https://matematiku.wordpress.com/2015/07/21/ln-phi-dalam-fungsi-hiperbolik/ see also : https://matematiku.wordpress.com/2015/07/22/ln-phi-continued-fraction/ ) #alisabanaconstant#alisabananumber#alisabana#prime#primenumber#bilanganprima#constant#goldenratio#rasioemas#eulerconstant#euler#logarithm#logaritma#naturallogarithm#numbertheory#teoribilangan#decimal#decimalexpansion#math#maths#mathematics#matematika
“e” = 2.718281828459045… JAIN 108 NEW FORMULA for the EXPONENTIAL FUNCTION
Jain 108 discovered a better way for defining the formula for “e” = 2.718281828459045 etc.This is the Exponential Number for nature’s growth and decay. “e” is the mathematical constant that measures the growth of human populations or viral colonies. It also is used in Compound Interest formulae, in Physics, it is used to establish the half-life of an element by studying its radioactive decay, and is used by coroners to predict the time of someone’s death for murder investigations.
It appears to act like the Phi Ratio, connected to biological systems, but is another separate entity, and is as important.I first Published this Discovery briefly in “In The Next Dimension” aka The Book of Phi, Volume 2, by Jain in 2003 but was received in 2000.In other Discoveries:Jain independently revealed the Infinitely Repeating 24 Pattern in the Fibonacci Sequence, by continued subtraction of 9 aka Digital Roots or Digital Compression.
He also discovered 2 important codes in the Wheel of 60 revealed when we continually subtract 10 from the Fibonacci Sequence, which is really observing the final or end digits, to show that a spiral pattern of these 60 infinitely repeating digits actually reEnters itSelf precisely on the 60th digit, and also that there is a hidden Harmonic 1111 and 6666 code embedded in the Wheel of 60… see the articles on this on this site.
There is great practical applicability to this Fibonacci 60 Code because Tesla knew that the 60 hertz or cycles per second in our electrical world is the most conducive for the human condition.The Pervasiveness of Phi (1.618033988…).
Jain can mathematical show that Phi is in all important systems, in biology, in crystals, in space, in atoms, and mathematically it is seen everywhere in the Doubling Binary Sequence (1-2-4-8-16-32-64), in the Pythagorean 3-4-5 Triangle, surprisingly in the Equilateral Triangle, in Magic Squares, in Prime Number Sequences etc.
C=2.718281728…UPDATE 1 on “e: Jain’s Discovery” Validated by Ewan Donovan “e’ has now been VALIDATED !
In my Instagram movie (igtv) I made a call to get assistance by computer-savvy technicians to improve the number of decimal places in e using my new formula. “e’ has now been confirmed for n =3,000,000 or 3 million Thanks to Ewan Donovan of the UK who sent me the latest update: e = 2.7182818284590…correct to 13 dp. (26th July, 2019) Previously, I had recorded n= 2,800 to get e precise to 7 decimal places: e= 2.7182818…to 7 decimal places.
Then Zevan Rosser‘s responded on my Facebook Business Page Jain 108 Mathemagics, improving “e” to 2 more decimal places, by plugging in n=20,000 giving the correct value of 2.718281828…which is 9 dp (decimal places). Then
Anthony Canosa, plugs in n=100,000 into my new formula and advances the 9 dp to 10 dp with the value of e=2.7182818284… Observe, that it only advanced 1 dp, from going from n=20,000 to n=100,000. It appears, that we have to plug in n=1 billion and 1 trillion. e = 2.718281828459045235… this is e correct to 18 dp as found in mathematical textbooks. Jain 108 (July 2019)
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