a mathematician crochets

As I have learned to crochet, my first thought is (as it is for all people, I assume): what is the mathematics involved in this beautiful fidget medium. Here are some questions I have asked so far (with answers, if I have found them):

Side note: Nothing would make me happier than other people engaging with these questions/trying to find answers/asking their own questions…. (:

  1. how do you tell how many yards of yarn there are in a ball, without just measuring it all?
  2. how do you tell how many yards of yarn a project will take, without just making it?
  3. knot theory things… (this is probably about a million questions, I know approximately nothing about knot theory, and am fascinated)
  4. weight vs. volume? Potential formula???
  5. making regular polygons?
    1. found this beauty: https://www.revedreams.com/crochet/yarncrochet/single-crochet-shaping-3-polygons/
    1. making platonic solids? I need to do it. There are only 5, after all. I can do that.
  6. mathematics of winding patterns for various yarn ball things…skeins, cakes, big ol’ knot, etc…
  7. mow does tightness of balling/density effect the ratio of final yarn length to weight (or some other measure)?
  8. how does material effect all of this? (density?) (Which size hook to use?)
    1. how does the size hook effect the final area of the piece?
      1. does that match with sizing? If so, US, UK, or metric? (side note: Why are there 3 different systems (according to the conversion chart that came with my hooks))
  9. How do types of stitches play into all this (single crochet, double crochet, half-double crochet (side note: terrible name. better name would be 1.5 crochet maybe?)

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