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MATEMATICAS: NUMERO DE EULER EN FUNCION AL PI Y AL PHI
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Réponse  Message 1 de 163 de ce thème 
De: BARILOCHENSE6999  (message original) Envoyé: 07/07/2017 17:15


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From: BARILOCHENSE6999 Sent: 21/04/2016 13:22


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From: BARILOCHENSE6999 Sent: 06/07/2017 23:00

The Language of the Divine Architect

The creation myths of many traditions describe the universe as the work of a Divine Architect who uses “sacred geometry” to unfold the dimensions of a beautiful cosmos, wisely designing every aspect of it, and governing by just proportions evidenced in the geometric shapes and processes of nature.

The language of God is mathematical language of numbers, proportions and (sacred) geometry.

“As Above, So Below” – these words circulate throughout occult and magical circles, and they come from Hermetic texts. The concept was first laid out in The Emerald Tablet of Hermes Trismegistus, in the words “That which is Below corresponds to that which is Above, and that which is Above, corresponds to that which is Below, to accomplish the miracles of the One Thing”

The entire Universe (including our solar system, as well as atoms, DNA and life-forms) reveals the secrets of balance, rhythm, proportion and unity in diversity, the fractal  interconnection of parts with each other and the whole. This harmony is expressed by some “key” numbers: Fibonacci Series, Phi, Pi and “e”.

The first 21 Fibonacci numbers:  
0     1     1     2     3     5     8     13     21     34     55     89     144     233     377     610     987     1597     2584     4181     6765

A simple number pattern, known as the Fibonacci Series, sits at the heart of  the marvelous architecture and patterns of life and growth.

These few equations are the “seeds” of  God’s “Grand Design” ( God’s “fingerprint”):

Pi = (6/5) * phi2

 Euler’s Identity Equation:

where
e   – is Euler’s number, the base of natural logarithms
i   –  is the imaginary unit, which satisfies i2 = sqrt(-1)
Pi – is the ratio of the circumference of a circle to its diameter

phi- is the the golden ratio number 1.618034

Mathematical beauty of Euler’s Identity

Euler’s identity is considered by many to be remarkable for its mathematical beauty. These three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:
The number 0, the additive identity.
The number 1, the multiplicative identity.
The number Pi, which is ubiquitous in trigonometry, the geometry of Euclidean space, and analytical mathematics (Pi = 3.14159265…)
The number e, the base of natural logarithms, which occurs widely in mathematical and scientific analysis (e = 2.718281828…). Both “pi” and “e” are transcendental numbers.
The number i, the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials (that are not constants), and whose study leads to deeper insights into many areas of algebra and calculus, such as integration in calculus.
Furthermore, in algebra and other areas of mathematics, equations are commonly written with zero on one side of the equals sign.

A poll of readers conducted by The Mathematical Intelligencer magazine named Euler’s identity as the “most beautiful theorem in mathematics”. Another poll of readers that was conducted by Physics World magazine, in 2004, chose Euler’s identity tied with Maxwell’s equations (of electromagnetism) as the “greatest equation ever”  — Wikipedia

 A simple number pattern, known as the Fibonacci Series, sits at the heart of  the marvelous architecture and patterns of life and growth.

 Pi and phi

Pi = (6/5) * phi2

 300 * Pi = 360 * phi2

For a circle with radius = 1 we get this equation for 
(close approximation of) its circumference:

2 * Pi = (360/150) * phi2

There is another way to write this equation:

Pi – Phi2 = 0.2 * phi2

Lets calculate the value:

Pi – phi = 0.5236
this number in meters is equal 20.614 inches = 1 Royal Egyptian Cubit 
(unit of length used by ancient Egyptians during construction of pyramids)

3:6:9

“If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.” –-N.Tesla

Perhaps Tesla had in mind another thing altogether.  It basically boiled down to energy/field/consciousness, which equates in to electricity/magnetism/consciousness, that made up Trinity. Energy is your divine spark, and field is the area you exist within. The 2 things that allow consciousness to isolate itself is electricity and magnetism. NOTHING in the physical universe exists outside energy and field…only then can you have consciousness reside inside a material existence.

3:6:9 … Perhaps these numbers were intentionally expressed by the pyramids of Giza…? There are 9 pyramids on the Giza plateau: 3 large pyramids and 6 small “satellite” pyramids. Also, the design of the Second (Khafre) Pyramid of Giza  is based on ratio 9:6.

Note: 6:5 is another special ratio used in ancient times

The Fibonacci series has a pattern that repeats every 24 numbers

Numeric reduction is a technique used in analysis of numbers in which all the digits of a number are added together until only one digit remains.  As an example, the numeric reduction of 256 is 4 because 2+5+6=13 and 1+3=4.  Applying numeric reduction to the Fibonacci series produces an infinite series of 24 repeating digits:

1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9

If you take the first 12 digits and add them to the second twelve digits and apply numeric reduction to the result, you find that they all have a value of 9.

1st 12 numbers:                                              1    1    2    3    5    8    4    3    7    1    8    9
2nd 12 numbers:                                             8    8    7    6    4    1    5    6    2    8    1    9
Numeric reduction – Add rows 1 and 2:             9    9    9    9    9    9    9    9    9    9    9   18
Final numeric reduction – Add digits of result:    9    9    9    9    9    9    9    9    9    9    9    9

This pattern was contributed both by Joseph Turbeville and then again by a mathematician by the name of Jain.

 
http://blog.world-mysteries.com/science/the-language-of-god/


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Réponse  Message 14 de 163 de ce thème 
De: BARILOCHENSE6999 Envoyé: 10/07/2017 02:54
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 02:55
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Réponse  Message 16 de 163 de ce thème 
De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:00
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:01
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:02
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:03
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Réponse  Message 20 de 163 de ce thème 
De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:07
Suddenly I have this idea that PI, the Golden Ratio and Euler's number could form a right triangle. I was almost right. Perhaps that's worth for someone.

 

Réponse  Message 21 de 163 de ce thème 
De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:08
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:09

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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:12
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:14
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:17
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:19
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De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:20
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Réponse  Message 28 de 163 de ce thème 
De: BARILOCHENSE6999 Envoyé: 10/07/2017 03:23


This article was initially posted at http://vixra.org/abs/1204.0102 on April 29, 2012.

You can also download the article in pdf format here.

Abstract

In this short note, the key to unlocking the secrets of quantum physics will be elucidated by exploring the fundamentals of Schrodinger’s wave mechanics approach to describing quantum phenomenon. We will show that de Broglie’s wave-particle duality hypothesis which lies at the heart of Schrodinger’s wave-function ψ produces a complex wave equation whose mathematical structure can be described by Euler’s famous equation {e}^{i	heta}=cos(	heta)+isin(	heta) which basically describes a helical wave in 3D space. By comparing and contrasting the electromagnetic wave with that of a helical wave which Euler’s equation represents, we may have discovered the geometric basis for spin and helicity and antimatter with negative energies that Dirac uncovered in his relativistic reformulation of Schrodinger’s equation.

Table of Contents

Section 1: Introduction

Section 2: Schrodinger’s equation

Section 3: Euler’s formula

Section 4: Electromagnetic wave

Section 5: Dirac’s discovery and insights

Section 6: Completing the quantum revolution

Section 7: Unknown Unknowns versus Unknown Knowns

Section 8: Conclusion

References

List of Figures

Figure 3.1. Euler’s formula and its connection to the sine and cosine waves.

Figure 4.1. This diagram shows a plane linearly-polarized EMR wave propagating from left to right

1 Introduction

In order to unlock the secrets of quantum physics, we have to go back in time and appreciate the challenges posed and faced by the founders of the quantum revolution. A careful reading of the ruminations of these founders as given to us in their Nobel lectures [1] leaves us with the feeling that something fundamental to their understanding was eluding them, as they were unable to see the key idea or concept that would have allowed them to FULLY appreciate the majesty and beauty of the quantum world. Even the last of these stalwarts Richard Feynman was dumbfounded, as reflected in his statement “I think I can safely say that nobody understands quantum mechanics”[2].

Using the same approach as was done in a previous note [3], we will go back to the basics and look at the founding assumptions and defining equations and their geometric representations, and attempt to find a pattern that lies at the heart of quantum physics by starting with the physicist who make the critical insight and the equation that was named after him. We will notice that it has a similar structure to Euler’s formula which can be represented geometrically by a helical wave in 3D space. This will then be compared to a classical electromagnetic wave in 3D space. Although both represent double harmonic oscillators, there is a distinct difference in the phase relationship that determines the physical characteristics that are found for the quantum of the field that they both represent. Finally we will discover that Dirac’s insights were already embedded in Schrodinger’s equation all along, and it was the lack of appreciation of this fundamental connection to Euler’s formula that was the stumbling block to the completion of the quantum revolution.

2 Schrodinger’s equation

Schrodinger’s equation [4] in its most general form can be represented as follows, where i is the imaginary number, hbar is Dirac’s constant or Planck’s reduced constant frac{h}{2pi},  frac{partial}{partial t} is the partial derivative with respect to time, psi is the wave-function, and hat{H} is the Hamiltonian operator:

(2.1)  ihbarfrac{partial}{partial t}psi=hat{H}psi

This equation was based on de Broglie’s hypothesis of the wave-particle duality, in which he ascribed wave-like representations, such as angular frequency ω and wave-number k to each particle. By using the Planck-Einstein relation E=hbaromega and de Broglie’s relation p=hbar k, Schrodinger discovered a wave-function psi that codified the energy E and momentum p of the particle to these wavelike representations, where A is the wave amplitude and e is the exponential function.

(2.2)  psi =A{e}^{i(k.r-omega t) }=A{e}^{frac{i(p.r-Et)}{hbar}}

It can be shown [4] that the time derivative corresponds to the energy operator hat { E } =ihbarfrac{partial}{partial t}, and the spatial derivative corresponds to the momentum operator hat{p} =ihbar
abla. By finding the eigenvalues of these operators that represent the observables, one can calculate the quantized energy and momentum of different systems. In effect, the utility and power of the wave mechanics approach rests on the identification of standing/stationary waves with the eigenvalue solving tools.

3 Euler’s formula

Euler’s famous formula [5] identifies the complex phase of the exponential function with cosine and sine functions:

(3.1)  {e}^{i	heta}=cos(	heta)+isin(	heta)

By comparing (2.2) with (3.1), and identifying with the wave-function psi=A{e}^{i	heta}, then the complex phase factor 	heta=k.r-omega t.



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