Hooking Up Manifolds

lorenz manifold

I love crochet. I spent a huge number of hours doing it when I was young, and only in later years did I realize that the same things that attracted it to me then are the same things that drive and motivate a lot of my research interests. (I many have mentioned this before, but it’s worth saying again).

It’s the love of patterns, plain and simple. If your child -of whetever gender- gets interested in any form of needlework, please don’t be shortsighted about it and to try to direct them away from the interest to other more “appropriate” things. You never know where it might lead to, and what they might discover on the way1.

So as you can imagine, I was delighted to see a Science News article about various mathematicians using crochet (hurrah!) and knitting (hiss!2) to construct models of various kinds of mathematical shapes (manifolds) in order to aid visualisation and benefit further research. The image above is a representation of a Lorenz manifold, for example, and this is an illustration (and such a cuddly one!) of hyperbolic geometry:

hyperbolic crochet

The artlcle goes a great deal into the story of how mathematician Hinke Osinga and her partner mathematician Bernd Krauskopf got into this, and why they find it useful. You’ll also hear from mathematicians Carolyn Yackel, Daina Taimina, and Sarah-Marie Belcastro. This has been going on for a while, and there are even published scientific papers with crocheting instructions for various manifolds! How did I miss out on this?! This is great!

Sarah-Marie Belcastro has a website about some of these matters here, although it is mostly about knitting, not crochet, but there are links to other pages and other “crafty” mathematics.

See Daina Taimina’s crocheting page too!

Now, somehow I think I missed picking up on this properly when I blogged about the excellent Insititute for Figuring (based here in Los Angeles) earlier in the year. In the comments, Bee actually pointed to some of the hyperbolic crochet figures there, and I looked, but I did not delve deeply enough. Now, from reading Diana Taimina’s site, I think the Iff’s interest in it stemmed from an earlier visit from her to talk about it. Have a look at their gallery.

I think I’m going to make some of these to decorate the house and the office!



1(Note to self – insert rant about them thanking their stars that it was not video games here? Probably not… someone will try to make the case that hours spent playing video games can lead to great things too. Can’t decide whether I’d agree or not. Best not to open distracting can of worms… end note to self.)

2 Just kidding. Childhood games and rivalries coming back to me.

Bookmark the permalink.

11 Responses to Hooking Up Manifolds

  1. Plato says:

    Layman scratching head. Interpretive look at the “art of science.”

    A “n-body problem” quantum dynamically perceived, or cosmologically, a “three body problem?”

    A “strange” abstract world to be travelling. 🙂

  2. Carl Brannen says:

    My sister is a knitter with tenure, and says that it provides useful stuff to do during various scholarly things. My inclination is more towards sewing, most recently wool suits, though I’ve not done any for years.

    There is also another hobby that is a bit like crocheting but more manly, and that’s the manufacture of chainmail, a hobby that if performed repeatedly will give you a grip strength like no other. (Smaller link diameters will be more work hardened, and the product will be stronger, and will also provide more exercise.)

  3. Harv says:

    A fellow crocheter (and scientist) here too. 🙂

    I saw those manifolds about a year or so ago and then in one of the Crocheting magazines, they had a pattern for a small hyperbolic manifold which I had to crochet. I figured it was an appropriate thing to work on during department talks and such. 😉

    Small picture:

    Large picture:

    I keep thinking it would make a great hair scrunchy or cuff for a jacket or something…

    I’ve also been wanting to make a Mobious (sp?) shawl I have a pattern for. 🙂

    And I’ve found a pattern for a crocheted Klein bottle too (which I haven’t gotten around to, but it’s on my list):

  4. Clifford says:


    Thanks! That’s great! How long did it take? Did your colleagues think you were mad?

    An idea: Do you know how to starch things? The old-fashioned laundry technique… That way, you could shape it a bit more easily and display it more dramatically. Just a thought.



  5. pedant says:

    The science/music nexus is widely recognised and celebrated (in this blog and elsewhere). It’s good to see the newly-cool knitting getting a look in as well; CVJ and Russell Crowe as celebrity tricoteurs – how hip is that. I’m a crochet man myself – my daughters taught me, in return for a bit of Mathematica(l) input to some of their design projects.

  6. Clifford says:

    Russell Crowe? I see. I’m going to have to start Fightin’ Round the World. 😀


  7. Harv says:

    Hi Clifford (sorry for the lateness, I was off at the AAS meeting)!

    It took me a few hours to do the small manifold. And well, I crochet a lot in talks around the department, so they didn’t think me any more crazy than normal. Thankfully, there’s a few knitters who do too, so that’s good.

    And I do know how to starch things (I’ve just started making snowflakes and doilies and such), but the manifold was out of regular yarn with small hook, so it does stand up pretty well. 🙂

  8. Clifford says:

    Aaaah… doilies. Used to make those a lot when I was very young. Happy memories.


  9. Pingback: Math on a tree « Qulog 2.0

  10. Pingback: Categorically Not! - Doing Darwin Differently at Asymptotia

  11. This is well cool! I was just thinking a couple of months ago that crocheting a Klein hat would be a good thing to do when I am too tired to work, but I got all confuzzled as to how to go about it. I see now that there are people who understand how to do these things, so perhaps I will go back to the project.