Christopher said to me the other day, 'Have you noticed that you get obsessed with things for two years, and then you get a new obsession?'

If I had just one child, I might have thought that remark was adorable and precocious.

Since I have 3 kids, I was somewhat .... annoyed.

So today I was telling Ed what Christopher had said, and Ed told me that Christopher asked him the other day what he thought my next obsession was going to be.

SAT writtten essay anyone?????

-- CatherineJohnson - 15 Jul 2005

Here's more evidence.

I used to knit CONSTANTLY.

All evening long, I would knit.

Watch TV & knit.

Now I do math.

I can barely get any knitting done at all; I have to tear myself away from math to knit.

It's not like I'm doing Higher Math, or Useful Math, or Lesson Planning For My Kids, or anything like that.

I am sitting around doing the problems in Russian Math.

-- CatherineJohnson - 15 Jul 2005

My friend Debbie, an artist who is Extremely Good At Math, told me, and I quote:

'Math is like knitting. Very relaxing.'

She is possibly the only person on the planet to think this.

Although, interestingly, that doesn't make her wrong.

-- CatherineJohnson - 15 Jul 2005

You're not a general Obsessive (well, okay, you are), but it's no wonder you love this stuff -- it's Knitting and Math, together in one topic!!!

-- CarolynJohnston - 14 Jul 2005

I think I'm going to make a Whole Separate Page on this subject.

That's the kind of Rank Obsessive I am!

-- CatherineJohnson - 14 Jul 2005

Mr. Fang has corrected me about the hyperbolic plane. To knit a flat plane (like a doily) you increase the same number of stitches every round. So for stockinette stitch, you'd increase four stitches a round, and that would make a nice flat doily. But it's not the same for a hyperbolic plane. Let's say you started with ten stitches. The first round, you'd increase five stitches. Then, as you knitted around, you'd still increase five stitches for every ten stitches already on the needle. So a hyperbolic plane gets very big in circumference very quickly.

But, as I said, it's really easy.

-- CardinalFang - 14 Jul 2005

All you have to do is knit or crochet from the center outwards. You figure out how many increases you'd need to make the knitting/crocheting flat, and then use more increases than that, so your project ends up with a saddle shape.

Actually, as a knitter, this makes perfect sense.

The folks on the NYC Math Forum were saying, a while back, that it's ashame all the shop & home ec courses went away.

If you want 'hands on' math, that's where you should get it.

Not collecting data for TERC.

-- CatherineJohnson - 13 Jul 2005

I'm going to enter Cardinal Fang's post in the index, under 'tips and tricks,' I think--and put this in the topic threads.

Thank you!

-- CatherineJohnson - 13 Jul 2005

All I have to say is I AM VERY GLAD I DID NOT TRY TO START A MATH BLIKI WITHOUT AN ACTUAL MATHEMATICIAN AS A PARTNER!

It would never, ever have occurred to me that sewing and/or crocheting a hyperbolic plane is easy.

As a matter of fact, I still have no idea what a hyperbolic plane IS, in mathematical terms.

-- CatherineJohnson - 13 Jul 2005

About ten or twelve years ago, Mr. Fang wrote a piece of software using hyperbolic geometry. He used to give talks about it, so he had me sew him a (piece of a) hyperbolic plane. It was easy, and took me about an hour.

Knitting or crocheting a hyperbolic plane is an easy task. All you have to do is knit or crochet from the center outwards. You figure out how many increases you'd need to make the knitting/crocheting flat, and then use more increases than that, so your project ends up with a saddle shape.

-- CardinalFang - 13 Jul 2005

math professor crochets hyperbolic space

Fantastic story in the TIMES today:

Dr. Taimina, a math researcher at Cornell University, started crocheting the objects so her students could visualize something called hyperbolic space, which is an advanced geometric shape with constant negative curvature....

...balls and oranges, for example, have constant positive curvature. A flat table has zero curvature. And some things, like ruffled lettuce leaves, sea slugs and cancer cells, have negative curvatures.

This is not some abstract - or frightening - math lesson. Hyperbolic space is useful to many professionals - engineers, architects and landscapers, among others.

[snip]

Math professors have been teaching about hyperbolic space for decades, but did not think it was possible to create an exact physical model.

[snip]

(This is my favorite part)
Dr. Taimina was a good candidate to create a better model. As a precocious child in her native Latvia, she tried her elementary school teacher's patience. When her fellow second graders did not understand a math lesson, she recalled, she would jump up and yell, "I can't stand these idiots," prompting her teacher to send notes home.

By high school she had settled down, and was most impressed by a teacher who was known to keep his advanced students laughing and engaged. When she became an educator, she decided that no student, regardless of aptitude level, would feel out of place in her classroom. One way she assured that was by using everyday objects to explain theories. (She was known for peering so intently at the oranges at her local grocery to see if she could find perfectly round ones to use in her geometry class that she scared the clerks.)

[snip]

In 1997, while on a camping trip with her husband, she started crocheting a simple chain, believing that it might yield a hyperbolic model that could be handled without losing its original shape. She added stitches in a precise formula, keeping the yarn tight and the stitches small. After many flicks of her crocheting needle, out came a model.

One professor who had taught hyperbolic space for years saw one and said, "Oh, so that's how they look"....

[snip]

A year after she created the models, she and her husband gave a talk about them to mathematicians at a workshop at Cornell. "The second day, everyone had gone to Jo-Ann fabrics, and had yarn and crochet hooks," said Dr. Taimina. "And these are math professors."

[snip]

As an adult, when terrified artists started showing up in her math classes to fulfill their degree requirements, she signed up for a watercolor class, thinking, "Then I will know how they feel."

Now when students tell her they simply cannot understand math, she pulls out one of her paintings and says, "I learned that in three months." Then she might pull out one of her crochet models.

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• Posted by: CatherineJohnson
• LogDate: Jul 11, 2005 @ 18:57

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META FORM	WebLogForm
META FIELD Title	Title	math professor crochets hyperbolic space
META FIELD TopicType	TopicType	WebLog
META FIELD SubjectArea	SubjectArea	CollegeMath
META FIELD LogDate	LogDate	200507111857