An Illustrated Classification of Knots.

Question

Let me be honest here: I know very little about Knot Theory. I'm sorry.

I've a friend though, someone with no training in Mathematics at all but who is a huge fan of knots (for whatever reason), who knows even less than I do about it, apparently. Thus I'd like a book or something as a gift we'd both enjoy: an illustrated classification of knots up to some large order, say, like this:

enter image description here ,

which I found here.

Do you have any ideas? They don't have to be books.

Please help :)

No need to be sorry man, I think we all want to know a little more knot theory. — jameselmore, Jan 16 '15 at 22:02
Not exactly an illustrated classification but: what about the little book "Knots" by Sossinsky? There are some nice pictures in there. — johndoe, Jan 16 '15 at 22:13

score 9 · Answer 1 · answered Jan 17 '15 at 01:00

9

The hand drawings in A Topological Picturebook by George K. Francis are second to none.

From Steiner's Roman surface to Boy's surface.

answered Jan 17 '15 at 01:00

Sammy Black

28,409

1

Thank you, although the pictures you have supplied aren't knots (as far as I'm aware prima facie) :) – Shaun Jan 17 '15 at 16:42
1

You're right, @Shaun, although the book is full of illustrations of knots, Seifert surfaces of knots, etc. – Sammy Black Mar 25 '15 at 19:28

score 8 · Accepted Answer · answered Jan 16 '15 at 22:05

8

I don't know about books... But if you think a piece of software can count as a gift, I suggest KnotPlot (http://knotplot.com/). It's a software package for creating, manipulating, and visualizing knots. The website has a bunch of nice examples.

answered Jan 16 '15 at 22:05

hasnohat

3,962
1
19
26

This is better than I hoped for, actually! Thank you! :) – Shaun Jan 16 '15 at 22:45

score 5 · Answer 3 · answered Jan 16 '15 at 22:17

5

The Knot Book by Colin Adams has a table of a lot of knots in the end, and is understandable for a non-mathematician who is interested in knot theory.

answered Jan 16 '15 at 22:17

user141592

6,206

score 4 · Answer 4 · answered Jan 17 '15 at 00:50

4

The Knot Atlas has various tables (of prime knots, of torus knots, of links, etc.)

The torus knot T(8, 3).

answered Jan 17 '15 at 00:50

Sammy Black

28,409

This is excellent! Thanks! :) – Shaun Jan 17 '15 at 22:05

score 3 · Answer 5 · answered Mar 25 '15 at 19:27

Jim Hoste and Jeff Weeks published a paper with Morwen Thistlethwaite entitled "The First 1,701,936 Knots" that tabulates prime knots up 16 crossings. The two teams developed separate methods and worked independently to create this census.

I particularly like Figure 2 on page 35 (reproduced below), which shows nice projections of knots up to 7 crossings. These projections show symmetries of the knots.

Knots up to 7 crossings.

An Illustrated Classification of Knots.

5 Answers5