# All Tied Up: A First Look At Modern Yo-Yo and Knot Theory **URL:** \ **Category:** General Yo-Yo\ **Created:** [August 21, 2025, 12:58am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623 "2025-08-21T00:58:51Z")\ **Posts on this page:** 18\ **Page:** 1
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 12:58am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/1 "2025-08-21T00:58:51Z")
As a part of my PhD my supervisor and I wrote a paper connecting 1A mounts with the mathematics of knots, check it out if that’s your jam 🙂 > **[All Tied Up: A First Look At Modern Yo-Yo and Knot Theory](https://arxiv.org/abs/2508.14462)** > > Modern Yo-Yo play has developed into a sophisticated international subculture, featuring elite competition and intricate tricks. Despite this, no systematic knot-theoretic treatment has yet been applied to the numerous string configurations realised... ---
**Author:** ![GTDropKnot](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/gtdropknot/32/212400_2.png) [@GTDropKnot](https://forums.yoyoexpert.com/u/GTDropKnot)\ **Post date:** [August 21, 2025, 3:51am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/2 "2025-08-21T03:51:49Z")
Yo this is dope. Way above my pay grade and i tried reading it but think I gotta wait until after my morning coffee tomorrow bc i was instantly lost lol. I think this kind of mathematics is what kim yeong min is studying bc they post stories with these kinds of knot images with the blue and red stuff I don’t know. They also make super super dope picture tricks. > **[김영민 Kim Yeong Min キム•ヨンミン on Instagram: "New trick at WYYC ⭐️🗼 @yjyoyoclub\_kr...](https://www.instagram.com/reel/DNIxhHTyKiU/?igsh=N3JwZGptcmN5NHF6)** > > 179 likes, 17 comments - kymyoyoer on August 9, 2025: "New trick at WYYC ⭐️🗼 > @yjyoyoclub\_kr @original\_throw @ultm\_kr > \#yjyoyo #prototype #originalthrow #otstring #newtrick #shorttrick #picturetrick #star #tower #doublegtcreators #trickcircle... ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 6:32am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/3 "2025-08-21T06:32:44Z")
So cool, I’ll check them out for sure! ---
**Author:** ![ice1000](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/ice1000/32/250979_2.png) [@ice1000](https://forums.yoyoexpert.com/u/ice1000)\ **Post date:** [August 21, 2025, 7:07am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/4 "2025-08-21T07:07:01Z")
Cool work!!! ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 7:24am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/5 "2025-08-21T07:24:56Z")
Legend 🪀 🪀 ---
**Author:** ![ice1000](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/ice1000/32/250979_2.png) [@ice1000](https://forums.yoyoexpert.com/u/ice1000)\ **Post date:** [August 21, 2025, 7:30am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/6 "2025-08-21T07:30:30Z")
Right now I’m at Def. 4.1 – very cool idea! And it seems to generalize nicely to 3A mounts too. How did you come up with the idea of hopping forward/backward? Is this a standard technique in knot theory? ---
**Author:** ![Tshou](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/tshou/32/611160_2.png) [@Tshou](https://forums.yoyoexpert.com/u/Tshou)\ **Post date:** [August 21, 2025, 7:36am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/7 "2025-08-21T07:36:06Z")
so freaking cool but ya know, me being mediocre at knot and tech tricks kind of adds up now, math was never my thing… ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 7:43am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/8 "2025-08-21T07:43:10Z")
@ice1000 Not standard as far as I know - I came up with it out of necessity really, I was trying to classify a GT and realised that actually I couldn’t until the loop was completed, and that there was a choice about how to complete the loop (since the yoyo was in contact with a string), so rather than pick a direction I figured I would just define both, since both are legitimate options in-play ---
**Author:** ![ice1000](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/ice1000/32/250979_2.png) [@ice1000](https://forums.yoyoexpert.com/u/ice1000)\ **Post date:** [August 21, 2025, 7:54am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/9 "2025-08-21T07:54:44Z")
That was exactly my argument on how knot theory cannot seem to be helpful in yoyos, but your solution is very nice. But the mount equivalence here is a bit too fine for yoyos in the standard sense, as you mentioned trapeze is considered the same as DoN/kamikaze. It’s very nice for classifying all the GT variations. In 3A though, this can be really really interesting, because you actually get a difference between the kink mount and a two-hand trapeze. ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 8:00am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/10 "2025-08-21T08:00:43Z")
100% the 3A case is on my to-do list for sure but need to make sure the extensions to links are all well-defined and there aren’t any situations one can encounter where the procedure needs to be refined ---
**Author:** ![ice1000](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/ice1000/32/250979_2.png) [@ice1000](https://forums.yoyoexpert.com/u/ice1000)\ **Post date:** [August 21, 2025, 8:27am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/11 "2025-08-21T08:27:22Z")
Actually, now that I think about it, two-hand trapeze and kink mount are equivalent, if you only consider double forward hopping and backward hopping. You can say that the trick trapeze pop to kink mount “preserves the mount”. But maybe not true when you consider one-forward, one-backward hopping. Is there any related theorems on this? The Minato ninja vanish GT will have the hopping-forward be a quadruple of u, and backward hopping something very very complicated. ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 8:39am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/12 "2025-08-21T08:39:23Z")
@ice1000 but if you double hop (either forwards or backwards) and don’t allow the strings to pass in front or behind one another (but immediately connect terminus to origin) then I think kink trapeze is still a Hopf Link and double trapeze is the Unlink. Trouble is it all depends on what the strings are allowed to do before the loops are closed, which is why I think a 3A theory would need to be quite precise in its definitions. The relevant theorems will be the link equivalent of unknotting numbers I imagine, but I would need to study it before I say that with confidence. > **[Unknotting number](https://en.wikipedia.org/wiki/Unknotting_number)** > > In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it. If a knot has unknotting number > > > > n > > > {\\displaystyle n} > > , then there exists a diagram of the knot which can be changed to unknot by switching > > > > n > > > {\\displaystyle n} > > crossings. The unknotting number of a knot is always less than half of its cros An... ---
**Author:** ![ice1000](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/ice1000/32/250979_2.png) [@ice1000](https://forums.yoyoexpert.com/u/ice1000)\ **Post date:** [August 21, 2025, 8:54am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/13 "2025-08-21T08:54:51Z")
I completely agree with the argument but I definitely know much less knot theory or topology than you. I’m excited for the 3A version of this! ---
**Author:** ![yoyo\_bambo](https://avatars.discourse-cdn.com/v4/letter/y/3da27b/32.png) [@yoyo\_bambo](https://forums.yoyoexpert.com/u/yoyo_bambo)\ **Post date:** [August 21, 2025, 8:56am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/14 "2025-08-21T08:56:30Z")
@ice1000 me too, 3A is my preferred play-style so I’m very motivated to head in that direction 🙂 ---
**Author:** ![Chaman](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/chaman/32/601454_2.png) [@Chaman](https://forums.yoyoexpert.com/u/Chaman)\ **Post date:** [August 21, 2025, 9:54am UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/15 "2025-08-21T09:54:47Z")
I have read the entire text and I found it very interesting. Automatically, the figures of the string games I used to make when I was a child came to my mind. [https://www.arvindguptatoys.com/arvindgupta/stringgames.pdf](https://www.arvindguptatoys.com/arvindgupta/stringgames.pdf) ---
**Author:** ![Jeaves](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/jeaves/32/203410_2.png) [@Jeaves](https://forums.yoyoexpert.com/u/Jeaves)\ **Post date:** [August 21, 2025, 1:57pm UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/16 "2025-08-21T13:57:01Z")
super cool man!!! nice paper and i like the method of constructing the mathematical knots from the mounts 💪🤟💪🤟 ---
**Author:** ![Xanadu](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/xanadu/32/84910_2.png) [@Xanadu](https://forums.yoyoexpert.com/u/Xanadu)\ **Post date:** [August 21, 2025, 2:33pm UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/17 "2025-08-21T14:33:15Z")
Very cool! 😎 nice work! ---
**Author:** ![Benthrowsyoyo](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/benthrowsyoyo/32/300522_2.png) [@Benthrowsyoyo](https://forums.yoyoexpert.com/u/Benthrowsyoyo)\ **Post date:** [August 21, 2025, 9:21pm UTC](https://forums.yoyoexpert.com/t/all-tied-up-a-first-look-at-modern-yo-yo-and-knot-theory/431623/18 "2025-08-21T21:21:37Z")
I just read this all the way through. Very interesting article, even if I don’t fully understand the concepts of topology. Thank you for sharing!