Talk:Ropelength

I was wandering whether we should use the term 'ropelength' as written together, since this is how most of literature, I have seen, used. Iswyn 02:24, 22 May 2007 (UTC)

First, thank you for writing this article. Second, I believe we should move to "ropelength". Someone moved the article to "rope length" claiming it was 10 time times more common in Google Scholar. However, when I looked in Google Scholar, it was clear a majority of the hits had very little to do with this knot theoretic idea of rope length, and even the ones that did were mainly not by knot theorists. A Google scholar search for ' "rope length" + knot' and weeding out extraneous hits (such as patent applications on rope using devices) is more revealing. In comparison, a Google Scholar search for "ropelength" brings up far more knot theoretic hits, and it's clear that many of the foundational papers use "ropelength". I would say the "10 times more common" claim is in favor of "ropelength". Since I cannot move pages yet, I will ask an admin to do so. --Horoball 02:04, 28 September 2007 (UTC)

The failure to include this information is abusive to the reader

$O(\operatorname {Cr} (L)^{3/4})\leq L(L)\leq O(\operatorname {Cr} (L)\log ^{5}(\operatorname {Cr} (L))).\,$

[Where L the length and L(L) is what???? Or where L is the knot and L(L) is the rope length of the knot?]

Michael Hardy (talk) 23:07, 6 July 2010 (UTC)

I agree that the notation here was really bad. I rewrote it to the best of my understanding but checking by someone more expert in the subject would be a good idea. —David Eppstein (talk) 00:58, 7 July 2010 (UTC)

Minimal rope length?

The article says 12 times as long as the thickness is too short to tie a knot. What's the minimal necessary length? And why doesn't the article either answer that question or say that nobody knows? Michael Hardy (talk) 23:08, 6 July 2010 (UTC)

New upper bounds and possible mistake

There are now better upper bounds for the ropelength of the trefoil knot, for example in Przybyl and Pieranski, High resolution portrait of the ideal trefoil knot, J. Phys. A: Math. Theor. (47) , 2014. I would gladly update it myself, but there is a factor 2 issue that I do not really understand: the bound in the aforementioned paper is 32.7429345. It looks to me that the bounds around 16 are for the ratio Length/Diameter instead of Length/Radius, but I am confused by the definition of Thickness here on Wikipedia which is somehow less intuitive, and for which there is also a factor 2 difference with the one in the paper "Quadrisecants give new lower bounds for the ropelength of a knot" for example. So actually it seems to me that with the definition that we use, the ropelength of the trefoil should be around 32 instead of 16, but I am afraid to correct it myself as I do not master this topic (in particular, the question would actually be more relevant with a 2 foot rope). Could anyone clarify this or tell me that I am wrong? Ventricule (talk) 15:50, 23 October 2014 (UTC)