
The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf] - lainon
http://math.harvard.edu/~ctm/home/text/books/adams/knot_book/knot_book.pdf
======
prideout
This is the book that inspired me to create a WebGL knot gallery
([https://prideout.net/knotgl/](https://prideout.net/knotgl/)) which I
eventually rewrote using Filament
([https://prideout.net/knotess/](https://prideout.net/knotess/)).

~~~
cogburnd02
1: That's pretty cool.

2: Would be nice if I could pause/slow down the rotation. Can't get the
Borromean rings to look like the Ballantine logo. (three interlocking perfect
circles.)

[http://mathworld.wolfram.com/BorromeanRings.html](http://mathworld.wolfram.com/BorromeanRings.html)

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dannykwells
I worked from this book extensively during my undergraduate thesis, and it was
an absolute joy to read and learn from. Compared to Lickorish ("An
Introduction To Knot Theory"), the explanations were easy even if you hadn't
had 3 semesters of graduate abstract algebra.

If you want a fun application of where knot theory can be used "in the real
world" there are some interesting applications to DNA untangling and the
function of DNA Topoisomerase - e.g.:

[https://sinews.siam.org/Details-Page/untangling-dna-with-
kno...](https://sinews.siam.org/Details-Page/untangling-dna-with-knot-theory)

[http://matwbn.icm.edu.pl/ksiazki/bcp/bcp42/bcp4216.pdf](http://matwbn.icm.edu.pl/ksiazki/bcp/bcp42/bcp4216.pdf)

~~~
lumberjack
I found this book a bit too informal. A very easy introduction to Knot Theory,
that is still mathematically rigorous is Cromwell's, one of the few books
written explicitly for undergraduates. After you are about 1/3 of the way
through, you can start using Lickorish. Combined they make the best
introduction, by far.

~~~
dannykwells
After 15 years of doing math, I've decided that, for myself, the best
introduction isn't the one that's "rigorous" or "in-depth", it's the one the
leaves you wanting to learn more. For me, that was Colin's book. I wish more
topics in math had entry-level books that explicitly helped contextualize
_why_ certain questions were being asked, rather than defining undergraduate
simply by what material is covered/how things are proved (of course, I ended
up as an applied mathematician, so it could just be me).

~~~
jkingsbery
I had a class with Adams while at Williams (multivariable Calculus, never got
to take his Knot Theory class). He was a great teacher, and excellent about
teaching students why they should care.

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pbk1
Wow - I took introductory topology with Colin just a few years ago. He wove in
a few examples from OP's book and I had several friends who took his knot
course - excellent resource for anyone interested and he is an amazing
person/mathematician.

Readers here might appreciate one of my favorite homework "problems" from his
topology course- it's a simple but counter-intuitive mathematical result
that's easy to replicate even for young children. Rip a sheet of paper (8.5x11
will do) in two long strips. Take the strips and tape them so that one is a
ring and the other is a Moebius strip.

Here's where the magic happens: make a guess about what happens when you cut
each object long-ways, then cut both objects with a pair of scissors. Won't
give any spoilers but the result may surprise you :)

EDIT: also forgot to mention the knot book and his topology book are great at
highlighting open/outstanding problems that precocious undergrads could
tackle. I definitely wish more authors of math texts went out of their way to
point out avenues for exploration like this.

~~~
posterboy
I will get two entangled moebius strips, right!?

~~~
pbk1
Only one way to find out!

~~~
dilippkumar
I am not a skilled person. I attempted this a bunch of times and all I have
are weird strips of paper.

Can someone please share pics if you got something other than weirdly shaped
strips of paper?

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mauvehaus
A non-mathematical, but much more practical resource, is the Ashley Book of
Knots (fondly known as "ABOK"). Clifford Ashley was a sailor who collected
knots, and an accomplished painter and writer. If you find yourself in New
Bedford, MA, you can see some of his work in the whaling museum (which I
highly recommend).

I took a knot theory class as an undergrad, and I don't remember which book we
used. It ended up being a pretty superficial introduction to the subject,
which is both disappointing, and probably also how I got my first "A" in a
math class since 11th grade (which, I would argue, was wholly undeserved)

Several key takeaways:

1\. The figure 8 knot is the only 4 crossing knot. If you climb, and use it as
your tie-in, you can check that you've tied it correctly by checking that you
have 5 pairs of strands in the knot.

2\. The figure 8 knot is amphichiral. There appear to be two variants (like
the left and right-handed trefoil knot), but they are transformable into each
other via the "pretzel" configuration, which seems to be the canonical
representation in math.

3\. If you coil rope with only overhand or underhand loops and pull it out,
you put a lot of twist into it. If you alternate overhand and underhand loops,
it pulls out untwisted. This is most easily seen with ribbon, which has two
distinct sides.

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geraltofrivia
This is a really nice introductory video (imo) on the topic by Up and Atom as
a guest on Tom Scott's channel.

Link to Video: [https://youtu.be/-eVd2Ugk9BU](https://youtu.be/-eVd2Ugk9BU)

Link to Up and Atom:
[https://www.youtube.com/channel/UCSIvk78tK2TiviLQn4fSHaw/](https://www.youtube.com/channel/UCSIvk78tK2TiviLQn4fSHaw/)

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shagie
For knot fans - there's also a code golf problem on Stack Exchange that only
has one solution so far - Knot or Not?
[https://codegolf.stackexchange.com/q/30292](https://codegolf.stackexchange.com/q/30292)

~~~
earthicus
The spectacular knot homology theories such as Khovanov Homology and Heegaard
Floer Homology can detect the unknot 'on the blackboard' as well. Wow!!!
Actually it can detect the genus of the knot: that's an amazing theorem! I
wish I understood how it worked :)

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z2
I got this book as a part of some math prize in high school. It's supposed to
give the reader a sense of appreciation of how knots can be modeled, and in
turn can even model other patterns. But when I learned sailing, I realized
that trying to read this book as a 14-year old contributed to an irrational
fear when learning to tie real knots.

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_emacsomancer_
Puts me in mind also of _The 85 Ways to Tie a Tie_
[[https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie](https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie)].

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case_of_snakes
No joke, I've been wanting an introductory book on this.

~~~
dsimms
Why Knot?
[https://www.amazon.com/dp/B00IF3UOQ4/](https://www.amazon.com/dp/B00IF3UOQ4/)

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te
What are the n most useful knots for sailors? Other outdoorspeople? Eagle
scouts? All-round handy problem-solver types?

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ianai
Very cool to see knot theory on HN! I studied it in undergrad and wrote a
paper about it as a class project.

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cphoover
I remember my highschool math teacher bought me this book.

