Saturday, September 15, 2007

Basset Knitter: Knitting Math Art With Escher Inspired Works

Basset Knitter: Knitting Math Art With Escher Inspired Works

I really enjoyed this post from Paula. Her readers are extending her ideas and seem excited to try the ideas. I commented that I knew of other math stuff she could knit and I finally found it. What's cool is that you can vary not just the yarn and crocheting-type things, but you can vary the math by making n equal any number you like: ". . . an increase is made in every nth stitch, so that the number of stitches from one row to the next is in the constant ratio, n:n+1."

You can also accent the structure of the plane by using contrasting or complementary colors. This sounds like fun and I hope one of Paula's readers, and other knitting and crocheting bloggers, will enjoy it. These planes would make great Christmas gifts. They look like the doilies that women have been crocheting for centuries. If you do this, please let me know!

What's a hyperbolic plane? "A hyperbolic plane is a surface in which the space curves away from itself at every point. Like a Euclidean plane it is open and infinite, but it has a more complex and counterintuitive geometry." This quote is from the article here that has a somewhat accessible discussion of what it is, what it looks like and how it behaves.

This site has photos and links to the other people that are crocheting the hyperbolic plane (you didn't think there were any, did you!).

Same title, different site. This one has directions for crocheting.
  1. Make your beginning chain stitches (Figure 2a). (Topologists may recognize that as the stitches in the Fox-Artin wild arc!) About 20 chain stitches for the beginning will be enough.
  2. For the first stitch in each row insert the hook into the 2nd chain from the hook. Take yarn over and pull through chain, leaving 2 loops on hook. Take yarn over and pull through both loops. One single crochet stitch has been completed. (Figure 2b.)
  3. For the next N stitches proceed exactly like the first stitch except insert the hook into the next chain (instead of the 2nd).
  4. For the (N+1)st stitch proceed as before except insert the hook into the same loop as the N-th stitch.
  5. Repeat Steps 3 and 4 until you reach the end of the row.
  6. At the end of the row before going to the next row do one extra chain stitch.
  7. When you have the model as big as you want, you can stop by just pulling the yarn through the last loop.
This site has actual crochet-type directions. It is from Crochet Magazine.

Make one of these when you tire of making hyperbolic planes.


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3 comments:

  1. I hate math, but I love to crochet and this really looks like fun. I've never seen anything like this before.

    ReplyDelete
  2. Wow! Thank you so much meeyauw!
    That is a very cool project!
    I just pulled up the pattern and I am going to give it a whirl! I will post my results soon.
    Once again I love your blog for the lessons I learn here.
    I was never very good at math in school and now that I am in my middle age of life I have been trying to re-learn the area I did not understand in school.
    This was a fantastic geometry lesson and now I get to make my own learning prop too!
    I think if I had you as a teacher in school I would have liked math more.
    My son is a math/physics major in college has been a great tutor to me lately and I am going to crochet these hyperbolic planes for him!

    ReplyDelete
  3. Oh Wow again!
    I just saw the site for the Lorenz Manifold and that is amazing! I am going to make that next for my son!

    ReplyDelete

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