3 ms·

I 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

by ksenzee 11y ago

I 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 ago
Which part was too technical?
- ksenzee 11y ago
  I 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 ago
    Yes, that's definitely poorly introduced, didn't notice that
  - ccpaper 11y ago
    The wrapping in cycles is where it lost me - is there a quick explanation of that?
    - Vragevuur 11y ago
      Yes, 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 ago
        I 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.
        Vragevuur 11y ago
        If the positions are marked like the numbers of the clock: "0 1 2 ... 11" Then with n = 5, the bags are placed like: "0 5 10 15 20 25 30 ..." which modulo 12 becomes: "0 5 10 (15-12) (20-12) (25-2*12) 6 ..." = "0 5 10 3 8 1 6 ..." As 5 and 12 have no common divisors, all positions will be occupied. Cheers

by ksenzee 11y ago

Vragevuur 11y ago

Which part was too technical?

ksenzee 11y ago
I 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 ago
  Yes, that's definitely poorly introduced, didn't notice that
- ccpaper 11y ago
  The wrapping in cycles is where it lost me - is there a quick explanation of that?
  - Vragevuur 11y ago
    Yes, 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 ago
      I 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.
      - Vragevuur 11y ago
        If the positions are marked like the numbers of the clock: "0 1 2 ... 11" Then with n = 5, the bags are placed like: "0 5 10 15 20 25 30 ..." which modulo 12 becomes: "0 5 10 (15-12) (20-12) (25-2*12) 6 ..." = "0 5 10 3 8 1 6 ..." As 5 and 12 have no common divisors, all positions will be occupied. Cheers