Knot Theory

firemath

firemath

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Has anyone here had experience with Knot Theory? If so, try to unknot some of these (try not to look at the solutions):

image.png
 
firemath said:
Has anyone here had experience with Knot Theory? If so, try to unknot some of these (try not to look at the solutions):

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What do you know about knot theory? If you know knot theory, perhaps I'll let you answer some of my Precalculus questions and give other tutors a break. Share your knowledge of knot theory with us. What is the name of the course that covers this theory?

Who is the creator of knot theory? What is the purpose in life of this theory? Why would anyone want to study knot theory?
 
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harpazo said:
What do you know about knot theory? If you know knot theory, perhaps I'll let you answer some of my Precalculus questions and give other tutors a break. Share your knowledge of knot theory with us. What is the name of the course that covers this theory?

Who is the creator of knot theory? What is the purpose in life of this theory? Why would anyone want to study knot theory?
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OP has posted a brain teaser involving knot theory. Either choose to answer or not, but there is no need to harass OP as you are doing.

You clearly have some issue with OP as they are the only one I've ever seen you respond like this to.

Keep it out of the public forums please.
 
I know almost nothing of knot theory but it looks to me just using visualization and experience w/rl knots that likely none of these can be unknotted without severing the cord, which I assume isn't allowed. Any knot can be undone if you sever the cord.

Am I missing something?
 
harpazo said:
What do you know about knot theory? If you know knot theory, perhaps I'll let you answer some of my Precalculus questions and give other tutors a break. Share your knowledge of knot theory with us. What is the name of the course that covers this theory?

Who is the creator of knot theory? What is the purpose in life of this theory? Why would anyone want to study knot theory?
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I'm not quite sure how to respond to this.
But, here goes:
Knot theory is a math branch of topology, the point of which is basically figuring out whether a mess of a tangles is just a mess, or a real knot that can't be unknotted. The tabular organization of these "planar diagrams," so to speak, is how scientists can use the data practically.
There are few practical applications, but they make fun paradoxes and practice problems. One of the applications is the structure of cells.
Carl Frederich Gauss created knot theory.
 
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firemath said:
Has anyone here had experience with Knot Theory? If so, try to unknot some of these (try not to look at the solutions):

View attachment 15425
Click to expand...
I think the important question is, what does it mean to "unknot" one of these? Apparently you got the image from a source that has answers; does it also explain what it means? Can you tell us the source?

One meaning would be to count the number of times you have to pass the rope through itself to produce an "unknot", as described here. Is that what you are asking us to do? Or are you asking whether they are all actually knotted?
 
Your description of pulling the rope through itself is what I am talking about...sorry for my late reply, I didn't see these posts at first.
 
firemath said:
I'm not quite sure how to respond to this.
But, here goes:
Knot theory is a math branch of topology, the point of which is basically figuring out whether a mess of a tangles is just a mess, or a real knot that can't be unknotted. The tabular organization of these "planar diagrams," so to speak, is how scientists can use the data practically.
There are few practical applications, but they make fun paradoxes and practice problems. One of the applications is the structure of cells.
Carl Frederich Gauss created knot theory.
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Did you paste and copy this reply? Do you really know topology?
 
harpazo said:
Did you paste and copy this reply? Do you really know topology?
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Whether the answer was copied/pasted - does not matter. You asked - "Who is the creator of knot theory? What is the purpose in life of this theory?" - and he answered. This is not a test in an academic course! Why are you being so "disagreeable"?
 
OK, I must admit I can't make heads or tails from this thread so far. No knot theory in my past. First question, what do the numbers mean? I'm guessing the numbers are the number of crossings, but what are the subscripts? What are we to do, untie them in our imagination or decide it it is impossible? "Try not to peek at the solutions". What solutions? Maybe a peek at a solution would be enlightening as to what the problem is since the OP certainly didn't properly pose it.
 
My MathWorld link (post #6) in effect gives the answers, and apparently is related to what the question was. But I, too, am still waiting to see where the image and question (about unknotting them) came from, where the solutions are that we were told not to look at, and, most importantly, what the question really is! It isn't clear what the OP knows, or wants to know.

The image is found in several places, including Wikipedia; but none that I have found talk about unknotting a knot. Another source, which has a good overview of the basics (more than I know), is https://girlstalkmath.com/2018/07/02/knot-theory-2/. Yet another is https://www.wikiwand.com/en/Knot_(mathematics).

@firemath, why haven't you helped clarify your question, but force us to try to figure out what your point was?
 
Dr.Peterson said:
My MathWorld link (post #6) in effect gives the answers, and apparently is related to what the question was. But I, too, am still waiting to see where the image and question (about unknotting them) came from, where the solutions are that we were told not to look at, and, most importantly, what the question really is! It isn't clear what the OP knows, or wants to know.

The image is found in several places, including Wikipedia; but none that I have found talk about unknotting a knot. Another source, which has a good overview of the basics (more than I know), is https://girlstalkmath.com/2018/07/02/knot-theory-2/. Yet another is https://www.wikiwand.com/en/Knot_(mathematics).

@firemath, why haven't you helped clarify your question, but force us to try to figure out what your point was?
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I'm waiting for Mr. Topologist to go deep into knot theory. Great to know that he has extensive math knowledge. I may need help with my self-study of Precalculus every now and then. You know, give MarkFL a little break??? So, Mr. Knot Theory, can you help me with graphing techniques aka transformation of graphs? Look over here=======> JUST KIDDING....
 
harpazo said:
I'm waiting for Mr. Topologist to go deep into knot theory. Great to know that he has extensive math knowledge. I may need help with my self-study of Precalculus every now and then. You know, give MarkFL a little break??? So, Mr. Knot Theory, can you help me with graphing techniques aka transformation of graphs? Look over here=======> JUST KIDDING....
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Who are these two people (plural) you are referring to?
 
Sorry for not replying. I have obviously not been on the site in awhile.

Presumably the answers can be found with a simple internet search. That's why was meant by "no peeking."
Dr.Peterson said:
The first one I find challenging is [MATH]6_3[/MATH]. How about you?
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I am rather stuck on 6 base 2.
 
Well, the minimum number of steps needed (the unknotting number) is shown in the first link I gave, so we know at least that much of the answer. (I really wish you would tell us your source, as I've still only guessed what your question meant. I haven't run across a site that actually shows how to unknot any of these, or that even poses that challenge.)

Since it says that 62 (I'd call the 2 a subscript, not a base) has unknotting number 1, all you should have to do is to flip one crossing at a time and see if the result is an unknot. (However, the page mentions that any particular drawing (projection) of a knot may not be unknottable in the minimum number of steps, though I don't know enough to fully understand that.)

Have you tried them all? Only one of them works, and it may well be the last one you'd try; it may require drawing it rather than doing it all in your head, as it can be a bit challenging to visualize.
 
harpazo said:
I'm waiting for Mr. Topologist to go deep into knot theory. Great to know that he has extensive math knowledge. I may need help with my self-study of Precalculus every now and then. You know, give MarkFL a little break??? So, Mr. Knot Theory, can you help me with graphing techniques aka transformation of graphs? Look over here=======> JUST KIDDING....
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Come, come, harpazo. No need to flame.
 
I hope someone has sent this to all the members of Slipknot so they can use these as designs for the next Knotfest
 
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