Home > Application, Appreciation > Mathematical Knitting

Mathematical Knitting

On the face of it, it’s hard to imagine two things as unrelated as mathematics and knitting.    And yet, here we have a website devoted to mathematical knitting:


A Klein-bottle hat (seen at right)?  A Mobius scarf?  Ingenious stuff, and a testament to our unlimited creativity and resourcefulness, if not our practicality.

The Klein bottle hat actually reminds me of the Klein bottle one of my students made out of plaster.

Click here to see more in Appreciation.


  1. June 13, 2011 at 10:01 am

    It’s only hard to imagine that math and knitting are unrelated if you’re not a knitter.

    The very first thing a knitter has to do when they sit down to make an object is “swatch”, which is make a small sample of the relevant stitch so they can see what their ratio of stitches and rows is to inches or cm. Making sure those ratios are right is the key to making a garment that fits.

    And people, being 3D objects not made of flat planes, also require curved surfaces in their knitting to make well-fitting garments. There’s tons of math in everyday knitting, even before you move into making abstract 3D objects (also cool).

    • June 13, 2011 at 10:02 am

      Sorry, I meant “it’s only hard to image that math and knitting are related if…”

  2. June 13, 2011 at 5:12 pm

    Thanks for the thoughtful commentary, Emily! I’m admittedly not a knitter, but I definitely see the algorithms there, and I can imagine how precise execution of those algorithms, and understanding of how each part fits in the whole, is crucial to a knitting project.

    I like your description of the “swatch”, making sure the ratios all work out. Sounds like similarity and dilation play a part there!

    Be sure to check out this cool mathematical knitting I saw on the street: http://mrhonner.com/2011/06/12/math-photo-knitting-the-plane/.

    • June 13, 2011 at 9:59 pm

      Yep – that’s actually the post that led me to this one… I subscribed to your blog in the last month or so — I love all the cool math photos and good thinking about teaching math, but missed your first knitting post until you linked to it today.

  1. June 12, 2011 at 9:07 am

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