Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What are...torus knots? Or: Wind p times, wind q times.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Thumbnail.
https://services.math.duke.edu/~psa/cls/611/knot53.gif
Main discussion.
https://en.wikipedia.org/wiki/Torus_knot
https://mathworld.wolfram.com/TorusKnot.html
http://katlas.math.toronto.edu/wiki/36_Torus_Knots
https://blackpawn.com/texts/pqtorus/
https://oeis.org/A051764
https://oeis.org/A002863
https://oeis.org/A086825
Background.
https://www.math.cuhk.edu.hk/course_builder/1920/math4900e/Adams--The%20Knot%20Book.pdf
https://en.wikipedia.org/wiki/Knot_(mathematics)
https://en.wikipedia.org/wiki/Knot_invariant
https://en.wikipedia.org/wiki/Braid_group
https://en.wikipedia.org/wiki/Reidemeister_move
KnotAtlas.
http://katlas.math.toronto.edu/wiki/The_Rolfsen_Knot_Table
SnapPy.
https://snappy.math.uic.edu/
Mathematica.
https://www.wolfram.com/language/12/math-entities/explore-torus-knots.html?product=mathematica
https://demonstrations.wolfram.com/TorusKnot/
http://katlas.org/wiki/The_Mathematica_Package_KnotTheory%60
Pictures used.
Pictures from https://www.youtube.com/watch?v=RAojTyfN3io&
https://services.math.duke.edu/~psa/cls/611/knot53.gif
Pictures from https://www.dtubbenhauer.com/lecture-geotop-2022.html
https://knotplot.com/knot-theory/torus-zoo-xing.jpg
https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/%283%2C_4%29_torus_knot.svg/220px-%283%2C_4%29_torus_knot.svg.png
Pictures from www.oeis.org
YouTube and co.
https://www.youtube.com/watch?v=RwXqkFnJ3j8
https://www.youtube.com/watch?v=zDzA7E7YGTw
https://www.youtube.com/watch?v=2dzJZx0yngg
#knottheory
#topology
#mathematics