Do you see patterns in Random Walks?
- Thread starter atlTrader666
- Start date
No, this is not Euler's identity. It is the equation that the golden ratio satisfies
phi^2 = phi+1
written as
phi = phi^2 - 1
coupled with the Euler identity
e^(ipi)+1 = 0 --> e^(ipi) = -1
you get
phi = phi^2 +e^(ipi)
so we all know who is the true mathematician here
Quote from intradaybill:
No, this is not Euler's identity. It is the equation that the golden ratio satisfies
phi^2 = phi+1
written as
phi = phi^2 - 1
coupled with the Euler identity
e^(ipi)+1 = 0 --> e^(ipi) = -1
you get
phi = phi^2 +e^(ipi)
so we all know who is the true mathematician here
Very, very good! Not very many picked up on that! I always use this equation to illustrate the relationship between phi, pi and e. I just love these kind of tricks to show the beauty of simple math.
What a nonsense one has to hear.
Why don't you use this one then :
phi^2 = phi + sin((n+1/2)x) / sin(x/2) - 2 cos(x) - 2 cos(2x) - 2 cos(3x) - ... - 2 cos (nx)
So you dare call Euler's identity "simple math". You must be a real genius.
Why dont you point us to a similar or better identity, with some deeper math and meaning, you have discovered ?
Tom
Quote from kut2k2:
While I agree that stating Euler's identity is pretty simple and it illuminates an elegant mathematical truth, actually deriving it would demonstrate the true mathematical skill.
Likewise anyone can say "E = mc²", but actually deriving it is an altogether different matter.
You can say it is "elegant", or that it is "beautiful".
But calling it "simple math" sounds to me as an insult to one of the highest achievement of human intellect.
When looking at these profound mysteries and beauty we must be humble and do not dare look down on them as they were "simple" for us, as if we could really have easily conceived them.
Tom
The first time someone successfully completes a complex task.
It is an amazing thing to view.
It is a thing of beauty and something to admire.
After one has successfully completedu 10,000 of these same complex tasks, each is still an amazing thing to view.
Each is no less an individual thing of beauty but the process becomes simple.
It is an amazing thing to view.
It is a thing of beauty and something to admire.
After one has successfully completedu 10,000 of these same complex tasks, each is still an amazing thing to view.
Each is no less an individual thing of beauty but the process becomes simple.
"Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there. "
The Character of Physical Law (1965)
or
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
The Character of Physical Law (1965)
or
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.