Intuitive Understanding Of Euler’s Formula

http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-190704
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On Feb 14, 8:48 am, "socra...@bezeqint.net" <socra...@bezeqint.net>
wrote:
>      Euler's Equation and the Reality of Nature.
> =.
> Mr. Dexter Sinister  wrote:
> ‘ I understand Euler's Identity,
> and I know what it means, and I know how to prove it,
> there's nothing particularly mystical about it,
> it just demonstrates that exponential, trigonometric,
> and complex functions are related.
>  Given what we know of mathematics it shouldn't surprise
>  anyone that its various bits are connected.
>  It would be much more surprising if they weren't, that would
>  almost certainly mean something was badly wrong somewhere.’
>
>     Mr. Gary wrote:
> Mathematics is NOT science.
>  Science is knowledge of the REAL world.
> Mathematics is an invention of the mind.
>  Many aspects of mathematics have found application
>  in the real world, but there is no guarantee.
> Any correlation must meet the ultimate test:
> does it explain something about the real world?
> As an electrical engineer I used the generalized
> Euler's equation all the time in circuit analysis:
>
> exp(j*theta) = cos(theta) + j*sin(theta).
>
> So it works at that particular level in electricity.
> Does it work at other levels, too?
> Logic cannot prove it.
> It must be determined by experiment, not by philosophizing.
> ====..
> Thinking about theirs posts I wrote brief article:
>        Euler's Equation and Reality.
> =.
> a)
>  Euler's Equation as a mathematical reality.
> Euler's identity is "the gold standard for mathematical beauty'.
> Euler's identity is "the most famous formula in all mathematics".
> ‘ . . . this equation is the mathematical analogue of  Leonardo
> da Vinci’s Mona Lisa painting or Michelangelo’s statue of David’
> ‘It  is God’s equation.’, ‘ It is a mathematical icon.’
>  . . . .  etc.
> b)
> Euler's Equation as a physical reality.
> "it is absolutely paradoxical; we cannot understand it,
>  and we don't know what it means, .  . . . .’
> ‘ Euler's Equation reaches down into the very depths of existence’
> ‘ Is Euler's Equation about fundamental matters?’
> ‘It would be nice to understand Euler's Identity as a physical process
>  using physics.‘
> ‘ Is it possible to unite Euler's Identity with physics, quantum
> physics ?’
> ==.
> My aim is to understand the reality of nature.
> Can Euler's equation explain me something about reality?
> To give the answer to this question I need to bind
> Euler's equation with an object - particle.
> Can it  be math- point or string- particle or triangle-particle?
> No, Euler's formula has quantity (pi) which says me that
> the particle must be only a circle .
> Now I want to understand the behavior of circle - particle and
> therefore I need to use spatial relativity and quantum theories.
> These two theories say me that the reason of circle – particle’s
>  movement  is its own inner impulse (h) or  (h*=h/2pi).
> a)
>  Using  its own inner impulse (h) circle - particle moves
> ( as a wheel) in a straight line with constant speed c = 1.
>  We call such particle - ‘photon’.
> From Earth – gravity point of view this speed is maximally.
> From Vacuum point of view this speed is minimally.
> In this movement quantum of light behave as a corpuscular (no charge).
> b)
>  Using  its own inner impulse / intrinsic angular momentum
> ( h* = h / 2pi ) circle - particle  rotates around its axis.
>   In such movement particle has charge, produce electric waves
>  ( waves property of particle) and its speed ( frequency) is :  c>1.
>  We call such particle - ‘ electron’  and its  energy is:  E=h*f.
>
> In this way I (as a peasant ) can understand the reality of nature.
> ==.
> I reread my post.
> My God, that is a naïve peasant's explanation.
> It is absolutely not scientific, not professor's explanation.
> Would a learned man adopt such simple and naive explanation?
> Hmm,  . . .   problem.
> In any way, even Mr. Dexter Sinister  and Mr. Gary
> wouldn't agree with me, I want to say them
>  ' Thank you for emails and cooperation’
> =.
> Best wishes.
> Israel Sadovnik  Socratus.
> =.
>  P.S.
> ' They would play a greater and greater role in mathematics –
> and then, with the advent of quantum mechanics in the twentieth
> century, in physics and engineering and any field that deals with
> cyclical phenomena such as waves that can be represented by
> complex numbers. For a complex number allows you to represent
>  two processes such as phase and wavelenght simultaneously –
> and a complex exponential allows you to map a straight line
> onto a circle in a complex plane.'
>
>    /   Book:  The great equations.  Chapter four.
> The gold standard for mathematical beauty.
> Euler’s equation.   Page 104. /
>
> #
> Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself,
>  but because it sharply points to our utter ignorance of the
>  simplest mathematical and scientific fundamentals.
> The equation means that in flat Euclidean space, e and Pi happen
>  to have their particular values to satisfy any equation that relates
>  their mathematical constructs. In curved space, e and Pi vary.
>    / Rasulkhozha S. Sharafiddinov . /
> ===============…

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