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)

The ancients selected the division of 360 degrees for a specific reason.

(Observe the outer ring of this complex Ying-Yang Chart having specifically 360 divisions).

The factors of the number 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 indicating that it has an unusually large range of divisors and therefore more friends with other numbers.…

So irrational! Euler's identity = e ^ (ix) = cos x + i sin x As cos (pi) = -1 and sin (pi) = 0, e^(i.pi) = -1 + i.0 = -1 Hence, e^(i.pi) + 1 = 0

Unfortunately, it had to be said, this is very incorrect.

With Circle's diameter, also equal to (A * G) = Real_Pi = 3.144605511...

A = Base Cathetus = Diameter / G = 1.94347308702659 Nowhere close to Phi....

And B = Opposite Cathetus = A * SQRT (G) = 2.47213595499959

To get the correct measure for a circle’s diameter and to prove that Golden Pi = 4/√φ = 3.144605511029693144 is the true value of Pi by applying the Pythagorean theorem to all the edges of a Kepler right triangle when using the second longest edge length of a Kepler right triangle as the diameter of a circle then the shortest edge length of a Kepler right triangle is equal in measure to 1 quarter of a circle’s circumference. Also if the radius of a circle is used as the second longest edge length of a Kepler right triangle then the shortest edge length of a Kepler right triangle is equal to one 8th of a circle’s circumference:

Example 1:

The circumference of the circle is 12 but the measure for the diameter of the circle is not yet known. To discover the measure for the diameter of the circle apply the Pythagorean theorem to both 1 quarter of the circle’s circumference and also the result of multiplying 1 quarter of the circle’s circumference by the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895. Divide the diameter of the circle by the square root of the Golden ratio = 1.272019649514069 to confirm that the edge of the square that has a perimeter that is equal to the numerical value for the circumference of the circle is equal to 1 quarter of the circle’s circumference.

Multiply the edge of the square by 4 to also confirm that the perimeter of the square has the same numerical value as the circumference of the circle.

Divide the measure for the circumference of the circle by the measure for the diameter of the circle to discover the true value of Pi. Multiply Pi by the diameter of the circle to also confirm that the circumference of the circle has the same numerical value as the perimeter of the square.

The second longest edge length of a Kepler right triangle is used as the diameter of a circle in this example. 12 divided by 4 is 3 so the shortest edge length of the Kepler right triangle is 3. The hypotenuse of a Kepler right triangle divided by the shortest edge length of a Kepler right triangle produces the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

According to the Pythagorean theorem the hypotenuse of any right triangle contains the sum of both the squares on the 2 other edges of the right triangle.

The shortest edge length of the Kepler right triangle is 3 and since the ratio gained from dividing the hypotenuse of a Kepler right triangle by the measure for the shortest edge of the Kepler right triangle is the Golden ratio of Cosine (36) multiplied by 2 = 1.61803398874989 then the measure for the hypotenuse of a Kepler right triangle that has its shortest edge length as 3 is 4.854101966249685. 4.854101966249685 divided by 3 is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895. The square root of the Golden ratio = 1.272019649514069

The square root of 14.562305898749058 is 3.816058948542208.

Remember that the second longest edge length of the Kepler right triangle is used as the diameter of a circle. The measure for both the second longest edge length of this Kepler right triangle and the diameter of the circle is 3.816058948542208.

Remember that the shortest edge length of this Kepler right triangle is 3 and is equal to 1 quarter of a circle’s circumference that has a measure of 12 equal units.

Circumference of circle is 12

Diameter of circle is 3.816058948542208.

Diameter of circle is 3.816058948542208 divided by the square root of the Golden ratio = 1.272019649514069 = 3 the edge of the square.

3 multiplied by 4 = 12.

The perimeter of the square = 12.

12 divided by 3.816058948542208 = Golden Pi = 3.144605511029693144.

4/√φ = Pi = 3.144605511029693144 multiplied by the diameter of the circle = 3.816058948542208 = 12.

The circumference of the circle is the same measure as the perimeter of the square.

4/√φ = 3.144605511029693144 is the true value of Pi.