3 ms·
Mathematics has probably already classified all knots that are human tieable. So from there you could iterate these knots in different physical positions, and p
by dexwiz 3y ago
Mathematics has probably already classified all knots that are human tieable. So from there you could iterate these knots in different physical positions, and perform different tests on them. The topological space has been investigated, now you need to decide between a teacup and a doughnut. This would be a mechanical engineering question, not a math question. Maybe look elsewhere?
- dekhn 3y agomath knots and real knots aren't the same thing and I don't think all possible human tieable knots have been enumerated and classified although I am happy to be pointed to evidence. Math knots embed circles while real knots are typically made with free ended ropes (although some knots are not). Math knots ignore friction and the width of the rope; real knots can't ignore friction and the width (and other phyhsical properties) matter. See the comment in this article https://en.wikipedia.org/wiki/Overhand_knot https://en.wikipedia.org/wiki/Overhand_knot While researching my answer I found out there's a term for what I wanted to do, https://en.wikipedia.org/wiki/Physical_knot_theory https://en.wikipedia.org/wiki/Physical_knot_theory I've had this discussion with mathematicians a few times now and they don't see the difference, so maybe I'm just missing something important.
- whatshisface 3y agoA knot with free ends can be turned into an embedded circle by connecting the ends far away from the knot. That's why they share a classification scheme.