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Hyperbolic Planes

HomekeepingGran

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FelixLake Collaborator

FelixLake

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I was just looking at those yesterday!!! Great minds think alike, I guess. I've never tried one, but they look like fun. The coral reefs are beautiful and you can get the instructions by purchasing the book. Too bad I have too many other projects going right now.

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Coffeywoman Explorer

Coffeywoman

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A year or so ago I crocheted the hyperbolic plane in earth tone stripes and had it hanging in a window. I think I got the pattern from an Interweave crochet magazine. (I should still have it somewhere.) But then a relative from Germany visited and liked it so much, it is now hanging in her window in Knittlingen apparently. And I hadn't been as diligent in those days about taking pictures of everything I make. I did it in fine yarn and crocheted fairly tightly as I recall, but I did like it and everyone seemed to appreciate it for its uniqueness.

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HomekeepingGran Proficient

HomekeepingGran

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I just found the Interweave pattern, Coffeywoman.

 

Huge Disclaimer: I AM NOT A MATHEMATICIAN or even remotely close to one, but I am familiar with Fibbonaci sequence which goes like this: 1+1= 2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, etc. The sequence occurs in nature all over the place. What I am now wondering is what a structure would look like if the increases followed one of the lower numbers in the Fibbonaci sequence, say, increase 2 in the first stitch and 3 in the next, then 2, then 3.

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LaurieE Enthusiast

LaurieE

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Thank you for sharing the link to the Interweave Press. I saw the article on the crocheted coral reef but I couldn't understand how to make one.

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HomekeepingGran Proficient

HomekeepingGran

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After looking around a bit, I realized that the popular spiral scarves are hyperbolic planes, so I suspect quite a few people here have made them but like me not knowing what they were mathematically. Remember the thread doilys which had extremely ruffled edges from the 40s or 50s. Those qualify, too. Curly Whirlies is a whole blog devoted to spiral crochet and knitting. Looks like fun! :D

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LaurieE Enthusiast

LaurieE

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Ever since I saw the crocheted coral reef a month or so ago, I've been fascinated with it and want to make one of my own.

 

I emailed Prof. Taimina looking for patterns other than the one that's posted. In her response, she directed me to the Interweave Press link. This is what she said:

 

"Idea of crocheting coral reef was born in Wertheim sister minds after they crocheted some of hyperbolic planes and then just let go mathematical rigidity. What is there in a reef - it is so called free form crochet - you just crochet not staying anymore in two dimensional plane - e.g. you just let your forms curl and be three dimensional. You can do it yourself just looking at some particular form and deciding where you would like to increase number of stitches and where to decrease. Just have fun and forms will emerge!"

 

I tried making one last night. I made something that looks like a corkscrew. Then I started on a second one that is going to take some time to turn into something.

 

I'm wondering if we shouldn't turn this into some sort of CAL.

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  • 3 weeks later...
LaurieE Enthusiast

LaurieE

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Mermaid -- Thanks for link!!

 

01buckler15 -- Sorry I didn't see your post sooner. Here's the link to the hyperbolic corkscrew I made. I didn't end off the yarn because I wasn't sure I was going to keep it.

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LeahB Contributor

LeahB

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Wow! This is so cool! I am really excited to see this! :clap I am a math professor, and actually had a colleague who had a student doing an independent study project on hyperbolic geometry this past semester. This particular student was looking at the connections between hyperbolic geometry and the work of M.C. Escher. (In some of his prints he used a model of hyperbolic space, called the Poincare disc) Anyhow, the student struggled a lot with trying to visualize hyperbolic space, and I wonder if having a crocheted model to experience might not have helped her. I may just have to make a hyperbolic plane myself to have around the department for students to play with in just such cases! What a find! Thank you!

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HomekeepingGran Proficient

HomekeepingGran

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I also sent these links to a friend in Africa who crochets. She got the hyperbolic plane bug, too, and is making models for a friend who "teaches math which is up in the clouds", she said.

 

OK, so have any of you seen the Lorenz Manifold model? (This is a PDF link; the photos are well down into the paper so scroll down to about page 16. Directions are here, too.) Gorgeous, just plain gorgeous. I could never force myself to count into the hundreds over and over to get this right, but my husband and I would love to have the Lorenz Manifold hanging in our living room! I guess I should say the Lorenz Manifold is a mathematical formula for how weather patterns behave. I'm not sure but I think it applies to both wind and water, but perhaps Leah can correct me here.

 

ETA here is a quote from a link on the Lorenz and its first crocheter:

 

Dr Hinke Osinga and Professor Bernd Krauskopf, both in Bristol University's Department of Engineering Mathematics, have turned the famous Lorenz equations that describe the nature of chaotic systems – such as the weather or a turbulent river – into a beautiful real-life object, by crocheting computer-generated instructions.

 

And here is a link for pictures of some other non-professorial crochters who have made the Lorenz.

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  • 3 weeks later...
dust Newbie

dust

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Sorry to bump such an old post but this is extremely interesting to me! I would love to participate in a hyperbolic CAL too. I think I've figured out how to make a plane but I am having trouble finding instructions on making one of the corkscrew ones if anyone can point me in the right direction I'd appreciate it. I've got to stop reading this forum, every day you guys give me a new project idea, I can't keep up! LOL

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Mermaiden Collaborator

Mermaiden

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Check it out... Lion now has a "pattern" (well, more like guidelines) for it for free.... :)

 

http://cache.lionbrand.com/patterns/c-coralReef.html

 

It's right here ;) ^

If you check in the PDF pattern, there's a corkscrew instruction/guideline too.

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dust Newbie

dust

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ok good, lol! I saw that link but it looked like it just said to make a chain and then increase back along it and you're done but they look like more than that from the picture. do I keep increasing as many rows as I want? maybe I should just wait until the baby goes to sleep and start messing with one and see what I come up with.

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iamnichole Explorer

iamnichole

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I got that issue of Interweave Crochet and started to make one of those but about 1/3 of the way thru it, I figured that I wouldnt know what to do with it when i was done and it was taking forever to get thru it, so i frogged it. But I never thought of hanging it in the window, so maybe I'll start up another one. I know they showed a girl wearing one as a scarf, but i didnt want to wear a math problem as a scarf. i'm just silly! forgive me!

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dust Newbie

dust

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well today I managed to make three hyperbolic planes and use up two old half skeins I had lying around, I think I've found a way to bust some of my stash! I'll try to post some pictures soon, I want to add some more to them first.

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clocke Apprentice

clocke

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I was just looking at those yesterday!!! Great minds think alike, I guess. I've never tried one, but they look like fun. The coral reefs are beautiful and you can get the instructions by purchasing the book. Too bad I have too many other projects going right now.

 

The book that you mentioned, is it A Field Guide to Hyperbolic Space by Margaret Wertheim?

 

HomekeepingGran, the Lorenz Manifold is beautiful! But I agree with you, the counting seems like it would be a beast. :lol

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