Intuitive Understanding Of Euler’s Formula http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-190704 =====….
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 . / > ===============… -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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