Category talk:Linked circles

It's in fact rather dubious whether all cases of linked circles are relevant to knot theory. The Olympic rings are certainly not very interesting from the point of view of knot theory. Furthermore, since knot theory is a branch of topology, it in fact makes no distinction between linked circles and other linked shapes... AnonMoos 16:19, 27 November 2007 (UTC)

I disagree. Olympic rings are linked circles. And linked circles are links, where the knots are (drawn as) circles. Hence they belong to the links and knots considered in knot theory. Whether they are important links for knot theory or not is irrelevant, they are links with certain additional properties. Also that, from the viewpoint of knot theory, the knots which can be deformed into each other are considered equivalent, is not an argument. In categorizing objects (two images) we should use the whole applicable (to the images) vocabulary. There will often be a higher category where both images belong to and where a difference between them, relevant for subcategorizing, will be considered to be irrelevant (circles and squares are images of the same topological space).

What is true is that the current category `knot theory' should rather be named `knots (knot theory)', and in `knot theory' there should only be images which describe techniques etc. from knot theory. Darapti

I have very little idea what you're talking about. It's certainly true that the Olympic rings are technically an example of a knot-theoretical "link", but it's actually an intensely boring link, about which there's extremely little to say, and which is certainly not an object of sustained interest to knot theorists. Furthermore, since knot theory is a branch of topology, it makes no distinction between linked circles and other linked shapes. From the point of view of topology, Image:Hallsberg_vapen.svg is exactly the same as Image:BorromeanRings.svg , but Image:Hallsberg_vapen.svg could not be legitimately be included in a category titled "Linked circles". If you wanted to establish a category Category:Knot-theoretical links , then you should have actually established a category Category:Knot-theoretical links , because a category named "Linked circles" cannot serve the same purpose which a category Category:Knot-theoretical links would serve... AnonMoos 12:28, 28 November 2007 (UTC)

Sorry that you did not understand my point. Whether something is boring can not be a reason that it does not belong to a certain category. Every mathematical category contains boring objects. Regarding the second point: The real numbers and an open interval of the real numbers are homeomorphic topological spaces (they are equivalent objects considered inside topology), but that does not mean that they have to be in the same category, in fact we should have intervals and real number lines separately, because they are not equivalent when considered as metric spaces (and in a lot of other respects). Darapti

In my opinion, this subject could be categorized in Category:Knots (mathematics), according to the English Wikipedia article Knot (mathematics). --Juiced lemon 19:06, 28 November 2007 (UTC)

I think that no category which includes the word "circle" in its name should be directly subordinate to "Category:Knot theory", because "Category:Knot theory" does not distinguish between circles and other shapes. Also, the fact that something is a "trivial case" or a "degenerate case" of something else is not really a strong enough reason to reorder category structures. Sure the Olympics rings emblem is technically a knot-theoretical link, but it's pretty close to being a trival or degenerate case -- there's really very little to say about it from the point of view of knot theory, and I would be surprised if it were the subject of any significant research. AnonMoos 20:01, 28 November 2007 (UTC)

Our job is to provide ways to find the media files for the illustration of Wikipedia articles. I have no doubt that some content of Category:Linked circles will be used in articles about knot theory. Therefore, in my opinion, we must allow browsing between Category:Knot theory and this category, despite your quibbling. --Juiced lemon 20:51, 28 November 2007 (UTC)

I wouldn't object to the Olympic rings being categorized in a Category:Knot-theoretical links (though such a classification would have very little practical value), but I do object to "Category:Linked circles" being put into "Category:Knot theory" because the Olympic emblem is a technically a knot-theoretic link. A category named "Linked circles" cannot fully substitute for a Category:Knot-theoretical links . AnonMoos 22:06, 28 November 2007 (UTC)

Sorry, we are not talking about the “link” theory, but about the knot theory. That's why the objects of interest are knots. A more serious objection would be that linked circles are not mandatory intertwined circles, while only intertwined circles (not glued ones) can concern the knot theory. --Juiced lemon 22:40, 28 November 2007 (UTC)

Not sure what you mean -- both single-loop structures (technically called "knots" in Knot Theory) and multi-loop interlinked structures (technically called "links" in Knot Theory) are of interest to knot theory. See the Knot theory wiki or "Knot Atlas": http://katlas.org/wiki/Main_Page -- AnonMoos 07:59, 29 November 2007 (UTC)

Your category proposal with an adjectival form (not used in Wikmedia Commons) appeared to me as a joke. More, knot theory amazingly don't define what is a link. So, I was wrong, and we can have as well Category:Links (knot theory) and Category:Knots (knot theory).

However, I meaned that the term “linked” in Category:Linked circles have no signification in knot theory, because it is only a term of common language. If you assemble two circles with bolt and nut, you get linked circles. --Juiced lemon 09:59, 29 November 2007 (UTC)