It's a nice video but it goes so fast I don't think people who don't already understand this stuff will get it.
Why does e to pi i equal -1? (2015) [video]
11–20 of 148 posts
Re: Why does e to pi i equal -1? (2015) [video]
#12Honestly the calculus explanation is the most clear to me (Taylor series expansion of e^x)
Re: Why does e to pi i equal -1? (2015) [video]
#13It's a nice video but it goes so fast I don't think people who don't already understand this stuff will get it.
Yeah, he's gotten much beeter about that since this video was released.
Re: Why does e to pi i equal -1? (2015) [video]
#14It's a nice video but it goes so fast I don't think people who don't already understand this stuff will get it.
"Young man, in mathematics you don't understand things. You just get used to them."
Re: Why does e to pi i equal -1? (2015) [video]
#15Is it pure chance that this was posted only two or three days after I watched it along with a few other e to pi = -1 videos? Randomness aside. 3blue1brown makes some wonderful math videos that I find really explain the intuitiveness of some of the ideas. I was unfortunately cursed with a math teacher who for whatever reason required us to memorize until we passed the test. Imaginary numbers were taught as "something…
Richard Feynman used to go up to people all the time and he'd say "You won't believe what happened to me today... you won't believe what happened to me" and people would say "What?" and he'd say "Absolutely nothing".
I agree wholeheartedly with the quality assessment of 3blue1brown videos. All mathematics should be clear and intuitive, by definition :)
Re: Why does e to pi i equal -1? (2015) [video]
#16e^x = an infinite series
if you substitute x = iz
you can split the even and odd terms of the infinite series into cos and sin
e^iz = cos z + i sin z
evaluating at z = pi yields
cos pi + i sin pi
-1 + 0i = -1
the exponential function maps the imaginary axis to the unit circle. pi gets mapped to -1.
This shows its true, but the "why" and real understanding requires calculus and the first week of complex analysis. Otherwise you are just parroting a set of facts.
Re: Why does e to pi i equal -1? (2015) [video]
#17[deleted]
Re: Why does e to pi i equal -1? (2015) [video]
#18It's a nice video but it goes so fast I don't think people who don't already understand this stuff will get it.
> goes so fast
Especially goes too fast right when it becomes less obvious.
Re: Why does e to pi i equal -1? (2015) [video]
#19At 2:37, right after finishing explaining adders and multipliers on the line it started going way too quick like where did e^x and some these infinite sums come from???
Re: Why does e to pi i equal -1? (2015) [video]
#20Gauss said that if the reason weren't immediately obvious to someone, they would never be a first rate mathematician. For the rest of us, there's YouTube.