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:

,

which I found here.

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

Please help :)

Answer 1

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.

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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.