What are some interesting project topics in Knot Theory?

I hope this isn’t something for /r/cheatatmathhomework, but I’m taking an introductory course in Knot Theory (for senior undergrads) and our last project is a 10 page paper on a subject in Knot Theory. I’ve thought for a while and come up with some ideas, but do y’all have any suggestions for an interesting topic in the field? Ones involving algebra would be even better. I’ve taken a few years of abstract and I know there’s a lot of algebra to explore in this field, but since my college didn’t make it a pre-req, our class doesn’t go into this much.

submitted by Nevin Manimala Nevin Manimala /u/DangerZoneh
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Please respect other people’s cars, and do not stand on them.

Begin rant.

https://imgur.com/a/rWnRa

Someone in a local car group recently posted about how his Miata has dents all over, peeled wrap, rip in his soft top, and footprints all over and I couldn’t help but feel for him for the complete lack of respect someone showed their property, especially a car.

However, with a little help from the group and some teenage stupidity, someone managed to dig up the culprits They felt that they should share with the world their quick guide on how to ruin someone’s car:

https://imgur.com/a/xPG1z

To add salt the the owner’s wound, many of the genius’ friends commented on how they were showing complete disrespect for the car, to which they replied “Lol it’s not even my car 😂”.

It’s not even my car yet I now have the fury of a thousand suns built up inside me after seeing and reading what this kid and his friends had done. I hope him and his friends get taken to small claims and pay every cent of the repairs needed to fix the damage they have done.

Please for the love of god do not ever stand on someone’s car. I cannot believe I even have to say this.

End rant.

submitted by Nevin Manimala Nevin Manimala /u/EnviousNacho
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Question about irrational-based number representations

First, forgive me, I’m not a mathematician, just curious.

A while back I stumbled on the Wikipedia page for phinary, the base-φ numbering system, and I sort of played with it as a curiosity because it’s super interesting and not intuitive (to me). I’ve been digging lately and learning a bit more about some of the other non integer representations like base-e and base-π.

I’m a physicist by training and had never explicitly encountered irrational-base representations prior to this. Between Google and Wikipedia the only practical use I can find is for Fibonacci coding as it pertains to data integrity. It’s really cool that the sequence has a sort of built-in integrity check. Wikipedia also gives the example of computing diameters and areas of circles in base-π which is cute but doesn’t seem as interesting or useful.

I was wondering if, other than the above, there were any known and useful applications of these irrational-base number representations? Are there any problems we know of that have interesting solutions or class of numbers that have interesting properties when approached in some irrational base representation? Or are these representations more or less academic curiosities for now? I can’t seem to find much on the arxiv but it’s possible I’m just not searching for the right terms or phrases.

submitted by Nevin Manimala Nevin Manimala /u/Inri137
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Things that I should not do when driving a V8?

Serious question.

I’m somehow concerned because I’m watched some meme videos of people with their mustang. I agree that it’s cheap and easy to get horsepower.. so people tend to underestimate it and mess it up. It’s my first time owning one and I don’t wanna fall under the same stereotype. I’d love to have fun with it at some point but in a really disciplined way. thoughts? do’s and dont’s?

I currently drive a 2018 Mustang GT (AT 10 spd). Almost second week of ownership, and I haven’t been to sport mode yet / turned off traction.

submitted by Nevin Manimala Nevin Manimala /u/5ekundes
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