5 ms·
The Medieval Fourier Transform
- tobr 11y agoIt might be obvious, but this should be read as a pedagogical explanation of fourier transforms, not as a historical account. From in the very end of the article: > Ok, you may doubt the historical accuracy, but the math is solid!
- carlob 11y agoObviously the round table's Percival/Parsifal is not really the one behind Parseval's theorem. https://en.wikipedia.org/wiki/Marc-Antoine_Parseval https://en.wikipedia.org/wiki/Marc-Antoine_Parseval https://en.wikipedia.org/wiki/Percival https://en.wikipedia.org/wiki/Percival
- srean 11y agoFrom the title I expected an article on pre-Copernican planetary models and its connection to approximation by Fourier series. Strangely enough that connection is not as popular as one would think in retrospect. It took me by surprise when I finally made the connection, "why the hell didn't I realize that before."
- jamessb 11y agoI don't think the connection is obvious if the fourier transform is simply presented through equations, but it is after seeing an animation like https://en.wikipedia.org/wiki/File:Fourier_series_square_wave_circles_animation.gif https://en.wikipedia.org/wiki/File:Fourier_series_square_wav... or http://blog.matthen.com/post/42112703604/the-smooth-motion-of-rotating-circles-can-be-used http://blog.matthen.com/post/42112703604/the-smooth-motion-o...
- kbart 11y agoMatthen's blog is really good one, he presents various math subjects in a very clear and illustrated way. My personal favorite: http://blog.matthen.com/post/111638712111/how-a-series-of-waves-with-increasing-frequencies http://blog.matthen.com/post/111638712111/how-a-series-of-wa...
- agumonkey 11y agoWhile I expected a wooden version of Michelson's analyzer : http://imgur.com/gyeR4A0 http://imgur.com/gyeR4A0
- Kinnard 11y agoThis is awesome. I'm sharing it with my niece and nephew! They're in grade school though . . .
- ksenzee 11y agoI would have guessed I had enough math to be in this article's target audience (two semesters of college calculus) but no. I think you have to have studied the Fourier transform already for it to make much sense.
- Vragevuur 11y agoWhich part was too technical?
- ksenzee 11y agoI don't think it's overly technical for its intended audience. It's just that it's written for an audience that understands phase, DC-component, main frequency, and what it means for something to be "wrapped in one cycle" around the table.
- Vragevuur 11y agoYes, that's definitely poorly introduced, didn't notice that
- ccpaper 11y agoThe wrapping in cycles is where it lost me - is there a quick explanation of that?
- Vragevuur 11y agoYes, it's just laying the bags in a larger number of rounds around the table. So first like the numbers of the clock, separated with 1/12 Then separated with 2/12, so two rounds Then 3/12 , thus three rounds etc.
- ccpaper 11y agoI thought I had it figured out like you described until the cycles were no longer evenly divisible into 12. From my (naive) point of view, the rule looked like when n=1 there are twelve evenly spaced bags around the table, when n=2 there are piles of two bags evenly spaced around the table, n=3 three bags evenly spaced, and so on but then you get to n=5. You can't put 12 bags into 5 even piles. That's when the whole example broke down for me. If I had to guess (keeping in mind I'm remarkably dense), I'm fixating too much on the piles. Maybe I'm supposed to be looking at superimposed circles. It might be less confusing to think about them unrolled into a line. When n=1, I have a line twelve months long and I put the bags evenly spaced along that line. Wrapping that line into a circle shows twelve evenly spaced bags. When n=2, I have a line 24 months long. Putting the bags evenly spaced along those 24 months, and then wrapping that line into a twice-looped circle would put the bags into piles of two. At n=5 the line is 60 months long. The bags are evenly spaced along that line and the line is wrapped into five circles, putting the bags into a wonky sort of arrangement, but that's just how it goes. I think that's what I'm looking at. Hard to tell without a marker and some yarn.