What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205
Added 2018-12-10 20:02:20 +0000 UTCGet a free crate for a kid you love (Awesome Chrsitmas gifts) at: https://www.kiwico.com/smarter
Click here if you're interested in subscribing: http://bit.ly/Subscribe2SED
⇊ Click below for more links! ⇊
Doga's a super smart dude who writes a Turkish blog "Bi Lim Ne Güzel Lan" that roughly translates roughly to "Science is Awesome Dude". We had a lot of fun working on this together. He would really appreciate it if you checked out his blog. The fun thing is that most of his articles transcend language.
Doga’s Blog (written in Turkish):
Doga’s original Fourier Series blog article that blew my mind:
http://bilimneguzellan.net/fuyye-serisi/
Click here to tweet him "thanks" for https://twitter.com/bilimneguzellan
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GET SMARTER SECTION
http://mathworld.wolfram.com/FourierSeries.html
Brady’s Video “Optical Tweezers and the 2018 Nobel Prize in Physics - Sixty Symbols”
https://www.youtube.com/watch?v=XjXLJMUrNBo
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tweet Ideas to me at:
http://twitter.com/smartereveryday
Smarter Every Day on Facebook
https://www.facebook.com/SmarterEveryDay
Smarter Every Day on Patreon
http://www.patreon.com/smartereveryday
Smarter Every Day On Instagram
http://www.instagram.com/smartereveryday
Smarter Every Day SubReddit
http://www.reddit.com/r/smartereveryday
Ambiance and musicy things by: Gordon McGladdery did the outro music the video.
http://ashellinthepit.bandcamp.com/
The thought is it my efforts making videos will help educate the world as a whole, and one day generate enough revenue to pay for my kids college education. Until then if you appreciate what you've learned in this video and the effort that went in to it, please SHARE THE VIDEO!
If you REALLY liked it, feel free to pitch a few dollars Smarter Every Day by becoming a Patron.
http://www.patreon.com/smartereveryday
Warm Regards,
Destin
Comments
Destin, I wanted to ask. Have you looked into path integration for quantum mechanics at all? I've finally been able to watch this video today, and it reminded me of another related challenge that mathematicians/physicists are struggling with. Most quantum mechanics is solved/analyzed using operators, most famously the bra-ket notation ( for example, the Hamiltonian of a wavefunction /Psi ). However, it was discovered some time ago that, if we know how to integrate over an uncountable infinity, we can actually use path integration (via the action integral) and functionals to solve quantum mechanics without almost any "fuzzy math methods" like bra-ket notation. There's a problem though; the only uncountable infinity we know how to integrate over comes from functional gaussians equations. And we only get functional gaussians from parabolic energy potentials (i.e. simple harmonic potentials). So the problem that relates to Fourier Series today is: can we use an infinite (or approximately infinite) sum of parabolas to map out other potentials, in the way that we do with the Fourier Series? I thought you might be interested in exploring this. Sorry for the tl;dr.
2019-04-15 17:23:12 +0000 UTCOh....you
Smarter Every Day
2018-12-18 16:39:52 +0000 UTCToday I learned Destin is the wrong side of the Gif Jif debate. I hereby rescind my Patreon membership. JUST KIDDING!
Adam Willcox
2018-12-11 23:12:17 +0000 UTCThank you for pronouncing it correctly, Destin.
Steve
2018-12-11 03:35:46 +0000 UTCI hate to say it, but you’re wrong Destin. It is a hard “g” like in “g”raphics. Love the video too. PS. I have a soft-spot for Georgia Tech. Applied and got accepted, but didn’t end up going there.
AJ Peck
2018-12-11 02:07:02 +0000 UTCAwesome Video, but I really want to see the equation the produces the symbol. I know it is probably something huge, but it would be nice to have a link to it.
Dan & Jen Baizel
2018-12-11 01:15:01 +0000 UTCThat was some gorgeous mathematics! But Destin, it's gif, NOT "jif"! (Unless you pronounce it Jraphics)
Kristy
2018-12-10 21:33:44 +0000 UTCWow - Just Wow!
Graeme Gets
2018-12-10 21:12:51 +0000 UTCSome interesting things out there: <a href="https://www.quora.com/How-are-neural-networks-related-to-Fourier-transforms" rel="nofollow noopener" target="_blank">https://www.quora.com/How-are-neural-networks-related-to-Fourier-transforms</a>
Tom Murphy
2018-12-10 20:25:20 +0000 UTCDestin... So you are saying Fourier series can approximate any function from data points... I work in AI, where we build Neural Networks which can also approximate any set function or set of data to any desired accuracy. Now I'm wondering if you or anyone else has heard of applications of Fourier series in AI or Machine Learning? (I'm guessing I'm not the first to think of this ... :) )
Tom Murphy
2018-12-10 20:19:56 +0000 UTCI don't know much Turkish, but I know that "Güzel" means "Beautiful", which might be even stronger - science is beautiful! And it truly is. I'll be watching your video in full with my family soon. Should be fun - and pretty.
Rosuav
2018-12-10 20:10:50 +0000 UTC
