Langles, Rangles & Tangles
A Blog of the trials and tribulations of Knot Theory
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In a Knotshell
Posted 1 days ago
Knot theory is a subset of topology! Topology is the study of shapes that can be stretched and moved while the main points stay the same. Knot theory is not only used in math but is also applied to science.
Comments view 5
Comments view 5
Eggy.Weggy
1 days ago
"Wayyyy more interesting than tying shoes"
--View 1 Replies
2C0ol4Sco0l
10 minutes ago
"Knutshell LOLL 🤣"
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Emma_G.
3 hours ago
"Wow! So smart!"
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T3chWizz//
7 hours ago
"that tangles mah brain 🥴🤭"
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SSSSSlithere
1 days ago
"okayyy but wher can u use this???"
--View 7 Replies
2.5k Likes
Knots, Links, & Crossings
Posted 2 days ago
These are some of the most basic aspects of knot theory and we thought that we should share them with you so you can gain some understanding too!
Links
Links
A link is several knots that don't connect or intersect each other.
The Unknot
The Unknot
The most basic knot there is, and has no crossings. It's front view look like a circle.
Knots
Knots
A knot is a closed loop in 3-dimensional space that doesn't intersect itself.
Crossings
Crossings
Part of a knot diagram in which two lines look like they are intersecting.
Comments view 6
Comments view 6
sixSeVEN.67
3 hours ago
"LUV the formatting you guys! keep it up"
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B@ller1naCAPPucin@
2 days ago
"Where can I get more like this?? still kinda new to this field :/"
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st_ORMY
1 days ago
"Does knot theory have practical applications?"
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Lilly.Draws_Things
2 days ago
"wow u guys must have a huge love of knots 😆😊"
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sooowhatsup
6 hours ago
"whats ur fav knot? mines the unknot cuz its easy :D"
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st_r_i.ke
7 hours ago
"is this taught in hs/middle bc i rlly wanna get into but idk how :("
--View 6 Replies
1k Likes
Reidemeister Moves
Reidemeister Moves
Posted 3 days ago
Sometimes it can be hard to tell if two knots are the same. Luckily we have the Reidemeister moves to help! The Reidemeister moves help us simplify knots and to compare them visually!
Reidemeister 1
Reidemeister 1
This move (R1) says we can add in or remove a twist in any knot to figure out what the knot is in its simplest form!
Reidemeister 2
Reidemeister 2
This move (R2) says we can pull strands together or push strands away from each other. This can be done in any knot to figure out what the knot is in the simplest form!
Reidemeister 3
Reidemeister 3
This move (R3) says we can pull strands pass crossings in any knot to figure out what the knot is in its simplest form!
Comments view 3
Comments view 3
fast_and.the.curious_
3 days ago
"I LIKE TO MOVE IT MOVE IT🐵🎶"
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Ella.1S_FAM0uS
11 hours ago
"me in gimnastics be like"
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user25739271
3 days ago
"tell me why I said Reed-Me-Stir"
--View 1 Replies
1.7k Likes
SOOO Many Whiteboards!
Posted 4 days ago
We've spent most of our time scribbling agressively on these bad boys. So please, enjoy our illegidble handwriting and maybe learn a thing or two about polynomials in Knot Theory!
Bracket Polynomials
Bracket Polynomials
The bracket polynomial modifies each crossing of the diagram so that we are eventually left with a collection of unknots. Since the unkot is equal to one, we turn it into a polynomial.
MORE Bracket Polynomials
MORE Bracket Polynomials
It was honestly a little tricky at first trying to understand the concepts. The polynomial itself is something that none of us have done before. But all four of us got it in the end!
Langles & Rangles
Langles & Rangles
Langles and Rangles have been the mathematical symbol of these past two weeks. Giving scary math symbols fun names, really gets you through it.
Comments view 7
Comments view 7
Xx.BRiT.Xx
4 days ago
"pictures in math are KNOT fun...."
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Knot.Into.Knots
4 days ago
"Never heard someone us Langle Rangle in a post💀"
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firstcleanpotato
12 hours ago
"Kaylee is sooo funny pls don't go bald..."
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its_gabiiii
3 days ago
"gabs, if ur hanwriting was up there, i would understand it so much more 😭🥺"
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RedFsh.Bluefsh
2 hours ago
"Langles and Rangles are soo cute :3"
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knot.luvr
23 hours ago
"Omg how do you make math fun?? Its KNOT working for me 😛💀"
--View 5 Replies
Kurt.Reidemeister
2 days ago
"Looking at this page makes me so happy :)"
--View 9 Replies
3.5k Likes
The Jones & Kauffman Polynomials
Posted 5 days ago
These are honestly our biggest opps, and we thought that we'd share them on here to see if anyone felt the same? Who knows maybe one of you could show us how to do it? The Jones, Kauffman, and Bracket Polynomials are all pretty similiar (you could even say they are LINKED). Here are some examples and definitions.
Comments view 4
Comments view 4
fickling_FunCTOR$
2 days ago
"whoa man"
--View 1 Replies
B!ngIT
3 days ago
"I respect doing it by hand but sometimes...you gotta just BING IT"
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th3c0l0r.r3d
8 hours ago
"where r the #'s?? 🤯😬"
--View 4 Replies
zestylem0$
11 hours ago
"Why??? huh? who?"
--View 7 Replies
2.6k Likes
Applications
Posted 6 days ago
When we were just starting out we all had the same question: "When are we EVER going to use this?" Well, guess what? We have found some uses for this abstract, unique, and theoretical side of mathematics.
Biology
Biology
Knot Theory can be helpful when explaining how enzymes disentangle
Physics
Physics
There is ongoing research on the connections of Knot Theory to Quantum Groups
Graph Theory
Graph Theory
Knot Theory can contribute to studies in Graph Theory, aiding in our understanding of complex numbers
Comments view 5
Comments view 5
Grrrr337
6 days ago
"Thats actually kinda interesting, never knew the uses till now"
--View3 Replies
couldntB3me
4 days ago
"Graph Theory? Quantum Groups? no freaking way dude."
--View 7 Replies
kristin.greylen
4 hours ago
"Quite informative if I do say so myself. After examining this particular post quite thoroughly, I am devoid of inquiry "
--View 5 Replies
MAKE.it
22 hours ago
"Aint no way, that's it? I thought there was gonna be sumthin else. BORING"
--View 8 Replies
huh
1 day ago
"i didnt get that could u say it again?"
--View 10 Replies
3.1k Likes
For More Information, Visit our Podcast and Presentation!
This is our podcast about Samantha Pezzimenti, a female mathematician who studies knot theory.
Girls Talk Math 2025 Knot Theory Group Presentation
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