12 ms·
I only skimmed the article and skipped to the 3Brown1Blue [0] video which I found very enlightening. Basically, the tldr version is that product under the inte
by abetusk 4y ago
I only skimmed the article and skipped to the 3Brown1Blue [0] video which I found very enlightening.
Basically, the tldr version is that product under the integral can be considered a sum, of sorts, in the Fourier domain (convolution <-> product and products turn into sums under some transformation of exponentiation) and when the coefficients of that sum cross a constant, then the original integral becomes less than pi.
That is, when $\sum_{i=0}^n \frac{1}{2 i + 1} >= 1$, that's the transition point. 15 in the denominator is where that sum is greater than one.
Awesome stuff.
[0] https://youtu.be/851U557j6HE https://youtu.be/851U557j6HE
- spindle 4y agoGreat summary explanation - thank you!
- quickthrower2 4y agoThat video is excellent and I wish they existed when I studied mathematics years ago as I may have kept going! In particular he gives the broad overview first so you understand it at a squint level and then you feel motivated to learn more. Vs. turning up at “Convolutions 101” lecture and having a lemma written on the board. This sort of math is my favourite advanced mathematics. I never enjoyed stats and I never enjoyed anything more abstract I could not visualize.