June 2020

A Summary of My Year of Mathematical Knitting and Crocheting

Now that 2012 is over and 2013 has begun, here is a summary of The Year of Mathematical Knitting and Crocheting.

Hyperbolic Space

  • Parallel lines and Triangles


  • A Pseudosphere and a Symmetric Hyperbolic Plane
  • A Hyperbolic Coral Reef – just for fun

The Möbius Band

The Klein Bottle

  • Constructed by knitting one Möbius Band and then “gluing” the edges
  • The Zipped Version
  • Constructed by crocheting two Möbius bands and then joining them.
  • The Zipped Version

Fractals and the Sierpinski Triangle

Seifert Surfaces (of the Trefoil Knot)

The Projective Plane


Patience and Perseverance

Last week, I bought a skein of wonderful, soft, shiny, dyed tencel yarn. It was a spontaneous purchase. The local yarn shop owner offered to wind the skein into a ball using the shop ballwinder. I agreed.

That was the first mistake. Such slippery yarn should never be balled using a ball winder. While winding it, the ball fell off the ball winder. The shop owner started winding the rest by hand. But 630 yards is a lot of yarn to wind by hand. She suggested I come back another day.

On Tuesday I picked up the yarn. The center pull ball looked sloppy. I decided to rewind it when I got home. That was the second mistake. Since the original was not well wound and the yarn so slippery, the ball fell apart. I had a tangled mess on my hand.

I was ready to give up. I was ready to go back to the yarn store, put the half balled yarn and remaining tangled mess on the “free” table.

But then I remembered that I had just bought the yarn. It wasn’t cheap. I still loved the color and the shininess of it. I still wanted to make a shawl from it.

So I sat down and started to untangle. That was Tuesday.

Wednesday, I untangled some more.

Thursday, I untangled even more. I was beginning to see some progress.

This was how far I got on Friday morning.

Do you see the ball of yarn? All that yarn was part of the tangled mess. By Friday morning, I had only a small amount of yarn to untangle. By Friday afternoon, I had finished. I have half the skein still on the ball winder and half the skein in a tightly wound ball. In another couple of days I will wind it all off the ball winder.

This was a lesson in patience and perseverance. I’m glad I didn’t give up.