fun fact: Bor means wine in Hungarian, and Wein means wine in German, so if you translate it, it's the winewine integral.
"a tiny positive number my computer couldn't compute in a reasonable amount of time" You should do it the Matt Parker way, put it up on the internet and people will improve your code by a factor of millions in a matter of days!
I'm a retired machinist and I ran into this twice this while machining radii from for example 9.500" to 8.500" in decrements of .01". I called tech support and no one knew the answer to this. They had never heard of it. Now I know, 15 years later.
I was lost before he began.
This is amazing. I even love the way you visually explained moving averages.
One of the main problems I have in making presentations is that I always try to make them like a story, avoiding spoilers so that everything leads up to the interesting take-home point, but you don't know what is coming until I get to it. This channel demonstrates why that's a flawed way of thinking for educational purposes. It's so much easier to follow along with these explanations knowing where they are going. The explanation at 4:22, while seeming like spoilers to me in the moment, was actually extremely helpful.
The next video on convolutions and their relationship to FFTs is out! https://youtu.be/KuXjwB4LzSA
I'm a retired electro-geek who last studied this stuff over 40 years ago. Having just discovered this channel, I wish I'd had this resource prior to slogging through the computational mechanisms available to us at that time. These verbal and graphical explanations are absolutely fabulous, and I foresee hours of enjoyable education in my future with a cup of coffee in one hand, these videos on my side screen, and a spreadsheet in front of me. Thank-you!
So if we alter the series with 1, 1/2, 1/4, 1/8, 1/16… the integral will always be pi since the sum of this series will always be less than 2
As an electrical engineer student as soon as I saw sinc(x) I immediately thought: Ah yes, definitely something with Fourier Transformation later in this video. Here we go again!
I've been trying to wrap my head around convolutions forever, so seeing that you're going to be doing a video about them has just made my day :)
this guy is the bob ross of math
Mathematicians: Math isn't mathing
Excellent ! That may also be an example of why proofs by induction are required : observing the first terms of a sequence never tells you for sure what happens next ...
As a Hungarian-German, the name Borwein is pretty funny: Bor in Hungarian translates to wine, and so does Wein in German. So their name is basically wine-wine
4:53 Oh shit. Grant is a gamer
me watching these videos to feel smart, knowing full well that i don’t understand a word he’s saying
Imagine testing a computer program for bugs and you find a bug in math
I don't know if anyone will ever see this comment, but as an Electrical Engineering student, I guarantee that Fourrier and Convolution are very powerful tools. We can analyze an entire circuit through equations modeled using fourrier and laplace. Note: I was taken by surprise, I wasn't even looking for videos on this subject.
@M4DA.