🧵 Untitled Thread
Anonymous at Thu, 14 Mar 2024 08:42:23 UTC No. 16073698
I have no idea what it means. I’m pretty sure nobody has any idea what it means. And it’s the most profound thing that I have ever seen in my life.
Anonymous at Thu, 14 Mar 2024 08:44:37 UTC No. 16073700
>>16073698
>I have no idea what it means.
>And it’s the most profound thing that I have ever seen in my life.
How do you know if you don't understand it?
Anonymous at Thu, 14 Mar 2024 08:47:56 UTC No. 16073703
>>16073698
https://www.youtube.com/watch?v=cUz
https://www.youtube.com/watch?v=qtI
https://www.youtube.com/watch?v=-dh
Anonymous at Thu, 14 Mar 2024 09:26:50 UTC No. 16073769
>>16073698
It's literally just junk rotating. Honestly I find the phase explanation most intuitive, but there's a bunch of ways to think about it.
https://www.youtube.com/watch?v=v0Y
Anonymous at Thu, 14 Mar 2024 09:27:06 UTC No. 16073771
Rotation of unit vector by 180° (π rad.) is -1. What's hard to understand? Not really "profound" or some shit
Anonymous at Thu, 14 Mar 2024 09:28:00 UTC No. 16073778
>>16073698
It's not a useful equation. It's just a natural consequence of complex numbers and polar coordinates. Nobody will ever invoke this equation to solve some other problem.
Anonymous at Thu, 14 Mar 2024 09:31:55 UTC No. 16073789
>>16073771
No, it is the most profound thing we have ever seen in our lives
Anonymous at Thu, 14 Mar 2024 09:58:51 UTC No. 16073859
>>16073698
I find it easier to explain by putting a 1 in front of the e to show its magnitude.
Anonymous at Thu, 14 Mar 2024 12:09:13 UTC No. 16074262
>>16073698
it's just a shorthand notation for >>16073769
Anonymous at Thu, 14 Mar 2024 13:10:58 UTC No. 16074780
>>16073771
Rotation with respect to what dimension?
Anonymous at Thu, 14 Mar 2024 13:17:01 UTC No. 16074831
>>16073778
The equation is useful for trigonometry, sinusoids, and converting between coordinate systems.
Anonymous at Thu, 14 Mar 2024 13:18:26 UTC No. 16074846
>>16074780
It's rotation in the xy plane about an axis in the z dimension often representing time.
Anonymous at Thu, 14 Mar 2024 13:25:36 UTC No. 16074957
>>16074846
Then why don't x, y, z, or t appear in the equation like they do in normal rotation formulas that involve x,y, z, or t rotations such as x = x cos θ + y sinθ and how does the imaginary dimension come into play since that is the only dimension explicitly in the formula?
Anonymous at Thu, 14 Mar 2024 13:32:37 UTC No. 16075076
>>16073698
Here: https://youtu.be/v0YEaeIClKY
If you have any interest at all in math, you should watch this entire channel. Grant is a genius communicator.
Anonymous at Thu, 14 Mar 2024 13:41:26 UTC No. 16075305
\>>16074957
>Then why don't x, y, z, or t appear in the equation
Because it's representing a relationship between the values at a fixed point. Specifically (-1, 0, π).
I think we can agree that another way the formula is written, e^(iπ)=-1 contains all three of those values, can't we? You could further rewrite it as e^(iπ)=-1+0i if you still need help.
Anonymous at Thu, 14 Mar 2024 13:56:38 UTC No. 16075647
>>16075305
How is a rotation a fixed point?
> e^(iπ)=-1 contains all three of those values
It doesn't contain any of the dimensions or planes you mentioned being involved in the rotation, but if you are just talking about for (-1, 0, π) e^(iz) = x + y, I still don't see how it is a rotation when rotations are more like x = x cos θ + y sinθ.
Anonymous at Thu, 14 Mar 2024 13:58:12 UTC No. 16075675
>>16075647
https://en.wikipedia.org/wiki/Euler
Anonymous at Thu, 14 Mar 2024 14:00:39 UTC No. 16075729
>>16073698
>this is your brain on youtube math
alternatively this is a low tier bait thread
Anonymous at Thu, 14 Mar 2024 14:07:01 UTC No. 16075844
>>16075675
The word rotation does not appear anywhere in the body of that link, there is just a reference to another theorem related to Euler at the bottom.
Anonymous at Thu, 14 Mar 2024 14:13:00 UTC No. 16075983
>>16075844
complex numbers definitionally involve rotation. i is literally 1 rotated 90 degrees.
Anonymous at Thu, 14 Mar 2024 14:19:58 UTC No. 16076144
>I have no idea what it means.
>filtered by high school geometry
Anonymous at Thu, 14 Mar 2024 14:27:52 UTC No. 16076286
>>16075983
Anything outside of x is literally 90 degrees from x, mathematically, but in reality, spatially, rather than just theoretically, what dimension does it rotate about?
Anonymous at Thu, 14 Mar 2024 14:28:44 UTC No. 16076303
>>16075844
So you are too retarded to actually read, and instead just use the CTRL-F strategy? I don't think you're ever going to get it.
Anonymous at Thu, 14 Mar 2024 14:33:11 UTC No. 16076408
>>16074262
That is not how you calculate the modulus, you moron.
Anonymous at Thu, 14 Mar 2024 14:34:13 UTC No. 16076440
>>16073698
>I’m pretty sure nobody has any idea what it means.
Because you are a complete idiot.
Anonymous at Thu, 14 Mar 2024 14:37:58 UTC No. 16076506
>>16076303
Why should I bother to read something that is unrelated to the question I asked that you only posted to appeal to authority because you know you are giving bad answers yourself and want to find an out instead of admitting you were wrong or don't actually know how to explain yourself?
Anonymous at Thu, 14 Mar 2024 14:42:30 UTC No. 16076579
>>16076506
>cos(x)+sin(x)
>how is it rotating???
Anonymous at Thu, 14 Mar 2024 14:59:55 UTC No. 16076750
>>16076579
see
>>16075647
x+y is specifically in the formula you gave, not sin or cos, and the rotation comes from the angle of rotation θ, not from adding the sin and cos of x.
Why can't you just explain how it is a rotation without memeing?
Anonymous at Thu, 14 Mar 2024 15:50:09 UTC No. 16077012
>>16076286
oh, you are that retard that believes that complex numbers can't be because we would then need 6 dimension(x, y, z, xi, yi, zi), god you are metaphysically retarded and detrimental for daring to waste the time of anons that attempt to comprehend what the fuck is wrong with you, keep at it, you genuinely do not deserve to shake of your retardation, you, how you are right now, in terms of intelligence, is how i desire you to die in the very far future, you do not deserve to evolve mentally in any way, shape or form
Anonymous at Thu, 14 Mar 2024 15:51:21 UTC No. 16077018
>>16077012
shake off* your
Anonymous at Thu, 14 Mar 2024 16:01:04 UTC No. 16077054
>>16077012
That is how orthogonality works, dimensions are all 90 degrees from each other, which you would already know if you had spent time studying instead of seething at boogeymen since you probably realized long ago that your rotation analogy is kind of retarded when you actually try to apply it to reality, but since you have no logical way to express your claims and are too proud to admit your retarded meme is retarded, all you can do is fixate on some past argument you clearly lost and still seethe about to this day which will probably also fester until you finally stroke out over it instead of admitting that your little 3d big bang model doesn't actually explain or allow you to understand everything.
Anonymous at Thu, 14 Mar 2024 16:09:19 UTC No. 16077084
>>16077054
>That is how orthogonality works, dimensions are all 90 degrees from each other
thank god you are stupid, to ayone else, enjoy >>16073703
Anonymous at Thu, 14 Mar 2024 16:17:47 UTC No. 16077108
>>16077084
So you think those axis are something other than 90 degrees from each other and you are calling other people stupid?
Anonymous at Thu, 14 Mar 2024 19:45:16 UTC No. 16077587
>>16073778
Polar representation is highly useful, whenever you're dealing with multiplicative problems in C.
Anonymous at Thu, 14 Mar 2024 19:50:49 UTC No. 16077597
>>16073698
>use series representation of exp to show: e^(ix) = cos(x) + isin(x)
>recognize that r(x) = cos(x) + isin(x) parameterizes the unit circle in C
>then calculate r(pi) = cos(pi) + isin(pi) = -1 + 0 = -1
>conclude e^(ipi) = -1
There you go. Once you have the series representation, it's a straightforward thing.