piranha | how i spent my friday

Very nice work!

p.s. femme: nice ruffles. butch: those aren't ruffles, that's a hyperbolic plane!

Yes! That's why I love mathematical knitting. (I just bought this book full of moebius based knitted shapes.)

They're good fun to make, aren't they? I do mine in cotton, so felting has never been an option.

I always get a bit annoyed at the Institute for Figuring stuff. I've been making hyperbolic planes since well before they first did, and I'm sure other people did too. If they could get over themselves in terms of "we made this fabulous new discovery" I'd deal a lot better.

Hello!

pleonastic said that you are quite into making hyperbolic planes. I'm going to try my hand at crocheting one and wondered if you have any tips, suggestions, or warnings?

I gonna use

pleonastic's pattern using cotton yarn - is that the same pattern that you use or do you have a different one? If a different one, any clue how the final plane might differ? Again, I'd really appreciate any advice you would be willing to offer. Thanks!

Tips, suggestions, warnings...

Well, firstly, the really practical stuff. Because I like quite a firm surface, and I think it's better for showing off the curliness, I crochet rather firmly, and most of my shapes only use single crochet. This is quite hard on my hands and I find I have to pace myself - no more than 15 minutes twice a day to start with, increasing gradually.

Secondly, I agree with

pleonastic about the slow, easy start that then suddenly explodes into endless rows. I think hyperbolic planes are great for giving you an idea of what exponential growth really means.

Nearly everything I've made has been circular, starting from a small loop (six single crochets over a doubled loop of the end of the yarn, and then carefully pulling the doubled loop tight). I like the flower/coral appearance of circular, and the simplicity of continuing around in a spiral without ever having to turn (I also like the appearance of that kind of crochet).

The "pattern" I use is just single crochet stitches in a consistent repeat: ranging from two stitches in every stitch (very curly, small diameter); through things like three stitches then two in the next (so four stitches becomes five every row); up to I think my maximum was 17 stitches then two stitches in the next (18 becomes 19 - this is a large diameter). For the large-diameter shapes, I do start with a small actual ring of chain, with about ten stitches on it - you get a long narrow tube, which is quite fiddly to work, and then suddenly it flares out into flat, and then it starts to flute at the edges.

(So, you have ten stitches in a ring, you go around the ring, single crochet in each, but that's still only ten stitches, so you go most of the way around the ring again, until you get to 18, which you then crochet into twice. Then you continue around your tube, ignoring what row you're on, just counting how many stitches since your last increase. To start with, the tube only widens by one stitch every two rows or so, but as it widens, the increases happen more often in terms of rows. You get a bit of a lump when you reach the row with 18 stitches, because your increases are now happening right near each other on each row, and not on the other side of the tube, but no-one else will notice it, and soon there are more than 18 stitches and the increases become spread around the tube again.

I think to start, you need to pick a consistent rule, such as

pleonastic's, (given it's working for you), so that you get a plane with constant curvature. (In fact, I think it's worth making two: a small-diameter and a large-diameter, because they show different aspects of hyperbolicness) But then you can muck around and do what you like, as long as you're clear that's what you're doing. What I mean is, constant curvature is not very intuitive, and if you're going for pretty, you will probably want to do something else, but it's worth knowing exactly what constant curvature looks like, and what it feels like to work.

I also like playing around with colour (as you can see): rings, and sectioning the circle into wedges (I carry the other colour inside the current colour), and using variegated yarn, as long as you don't mind weird blobs, as your stitch count comes into synch with the colour repeat, and then goes out of synch.

I have no idea if that's the kind of stuff you wanted to know.

Thanks! This is the sort of info I was asking for!

As far as crocheting firmly, I don't think I'm capable of that at this point - but maybe as I get better at it I'll be able to make tighter, more even stitches.

I'm having some trouble with my turning stitches at the moment, so maybe I will start with a circular pattern instead. It's just been so long since I've done any crocheting that, for all intents and purposes, I'm having to relearn everything.

The 17 then increase pattern sounds like it would end up looking like one of those trumpet flowers - those are very pretty. I could also imagine turning something similar to that into a hat.

When you suggest making a "small diameter" and a "large diameter", do you mean make one with, for example, two stitches in every stitch and then make another with, for example, 17 stitches then two stitches in the next - that is what will change the diameter?

I think, at this point, I'm more interested in 1) getting down the basic crochet stitches and 2) learning about constant curvature.

I have some varigated, cotton yarn that I'm using. It seems to be working best for me as far as clearly seeing the stitches that I'm making. The varigation goes from white through several shade of pink. I figure, I can use a solid, dark pink as the final few row, like you've done in your icon with the green.

Do you have any other pictures of your work posted? I'd love to see the different variations that you've worked on!

Thank you again for the reply - I really appreciate it!

Yep, the pattern with a long repeat before the increase does give a trumpet flower, or hat, or gravity well model (I made one for my friend who's an astrophysicist).

Again, yes, small diameter = frequent increases = very curly, and opposite for large diameter. It's hard to explain but very obvious when you're doing it, which is why I recommend making them to see.

I don't have many pictures. Most of my hyperbolic crochet was done in the late eighties and early nineties - I don't think I had a camera, and certainly, no-one took pictures of everything the way you can now. I gave a lot away. I think one of the things I resent about the recent fuss is that now they've become "valuable" and learning experiences and I really liked just making them and giving them to people who were intrigued by them. (So they were learning experiences, but much more subtly).

So I fished out the pictures I have of the two most recent ones (they're in my craft gallery - I haven't used LJ's picture facility before so I may have stuffed something). The purple one is increase in every stitch, I think, and the yellow-green is something like two or three stitches between increases. I haven't made any trumpets while I've had the digital camera.

Wow, the purple one is super curly - like a little ball of curls! The one I decided to start with is three single crochets, then one increase stitch. That should turn out, I think, like your yellow and green one - except I decided to do a plane, because I couldn't remember how to start with a circle and couldn't be arsed to get up and grab my crochet booklet.

Next time I'll do a cirle and I'll probably make a gravity well, just because that sounds awesome. Providing, of course, that I survive making this initial effort.

As for your philosophy on making these, I get it. I have this loom-thingee on which I make these really nice scarves. I'm sure I could probably sell them at a craft fair, but I'm totally fine just handing them out to people I know. I gave one to this girl I work with. Later, someone said to me, "I didn't know you knew her that well," and, the truth is, I don't, but the color suited her and she wanted it and I was very happy to give it to her.

So, I think it's cool that you gave them away to people who wanted them and found them useful. I can see how it would be instructive to make one yourself, especially if you're studying something that pertains to hyperbolic planes, but not everyone is crafty or would enjoy the process.

Me, I just like how they curl and I want to practice some basic crochet stitches and I really needed something to do on my lunch break each day.

Up to this point, I've been starting and stopping and pulling out stitches, but tonight I made a go at it under some good light and I think I finally am getting the hang of it. I have a nice, flat plane that's already splaying out at the sides - it was just a matter of really looking at the stitches and paying attention to what I was doing! The varigated yarn is actually helping me figure out my stitches, too, much more easily than the solid color I was working with initially. I'll save the solid color for the end - by that time, I ought to be able to work these single crochet stitches in my sleep!

Thanks again for helping me with this. I'll keep you posted on my progress, if you want.

I'm glad you're making progress and I'd be happy to hear (and see) how it all works out - provided

pleonastic is okay with it all :-).

completely fine. in fact i want to know about it; i am just not doing anything else with it myself right now, but i am still interested. and i am glad you posted peectures!

Hee - I've added just two more rows to my still-tiny hyperbolic plane, but already the edges are getting curly. It looks like a small cuttlefish!

Oh, I want to make one of these!! I've done a little crocheting, a long time ago, and have completely forgotten the lingo. Could I ask you for a little help?

How many stitches did you begin with in row 1? How much yarn did it take to make the hyperbolic plane in the picture? Have you tried a hyperbolic circle instead of a plane, just going round and round, instead of turning at the end of each row?

This isn't quite the same pattern I've seen listed elsewhere. On this page (http://www.math.cornell.edu/~dwh/books/eg99/Ch05/Ch05.html), the pattern calls for just a chain stitch and a single crochet stitch. Have you tried this pattern? How do you think this pattern will end up looking compared to your picture above?

heya!

sorry for the delay; i was trying to find my notes. but *wah*, i didn't. so i can't give you too much information: like i don't remember how much yarn i used (i did write it down, but where?). the type of yarn, because i wanted to felt it (haven't done that yet) was paton's "classic wool", which felts relatively evenly in both directions. i used less than one skein (they're 100g each, and run for 204m) because i had already used part of that skein for another project, but i don't know how much. oh hey, wait -- i can weigh it! 55.7g, so a bit more than half of that skein.

i started with 2 chain stitches and then a single crochet into the first of those. my pattern will curl less quickly than the one on the page to which you linked. no, i haven't tried a circle. there's somebody on my flist who's quite into hyperbolic planes and has done more than i, maybe she wouldn't mind talking to you about her experiments:

aquaeri.

oh i see you like torchwood. mmmh! i really got sucked into that right before my more recent obsession with anime; should really write about it.

Thanks for writing me back!

I definitely have that much spare yarn laying about (though, it's cotton), so I should be okay. Thanks for letting me know how you began.

I tried the pattern on that other page, but ... I don't know, it just didn't seem to be coming out right. I'm going to give your pattern a try instead; even if it doesn't curl as quickly, I still like the picture, so if mine turns out anything like that then I'll be happy.

Thanks for the link to

aquaeri - I'll check out her journal.

Also, Torchwood! Yes, I wasn't sure I was going to like the show, but I was a complete gonner by the last ep and now can hardly wait for more! I'm really curious where they're going to take Jack's character in the next TW season, especially since he's guesting in a few eps of the next Dr. Who season and reuniting with the Doctor should have a profound affect on him. I'm oh-so-curious!

making the plane was really instructive about logarithms; i wish they had used something like this in school. for a while there it's just short rows going back and forth, easy-peasy. and then suddenly the rows seemingly have no end, *slog*slog*slog.

you can't see it in that picture, but one could actually sew the sides together and create a cone shape with ruffles that way. i'm thinking of making a hat by varying the pattern enough to create a form-fitting shape for the head. :)

yeah, torchwood turned out to be a positive surprise for the most part, and made me want to watch DW again, at least those parts where captain jack appears (i am still pouting that christopher eccleston left after just one season). i don't like all the episodes of torchwood, but enough of them to keep wanting to watch. even though they killed suzie! :)

I think you could make an awesome hat out of this! You could either sew up the two sides or you could start crocheting from a circle instead of a flat row. Either way, I think the final curly edged brim would look very cool.

I'm not really looking forward to the slog*slog*slog part of this, but it will certainly be good practice for making my stitches even.

I agree about TW having an...uneven season - some eps were definitely better than others. But, they've had 13 eps to get all the characters and inter-personal dynamics figured out, so maybe we'll get a more consistant product next season? But, I sort of felt the same way about the first half of the first new season of Dr. Who - I don't think they really hit their stride until later and, then, Eccleston left! He really should have done at least one more season. Has he ever said why he only did one?

yeah, i'll make the hat in a circle, i think -- i generally do that because i am lousy at finishing things, and can never look a crochet seam look decent enough.

that's what the slogging is definitely good for. i ended up doing it while watching tv, *heh*, but i've crocheted for a long time so it's pretty automatic. i think it's great that you're getting into these -- i really like the intersection between math, art, and craft, it's so ... elegant.

i think i read eccleston left because he didn't want to end up being typecast, but i don't even recall whether that was anything official.

i've only watched torchwood up to where they bring suzie back; i should catch up once i am through my anime backlog. oh, and i really like the opening theme, i wish it were longer. wonder whether there's a soundtrack out yet.

yeah, i'll make the hat in a circle, i think

That sounds like an excellent plan. I want to make one, too - not to use as a hat, but something circular with a lot of stitches between increases. I'm guessing your hat would look awesome with a pom-pom on the end of it!

And, yes, I agree about the elegance of math, art, and craft - I used to quilt and it comes into play heavily there as well.

As for Christopher Eccleston, I don't see how he could be type-cast by doing the Doctor for a few seasons - he's had such a long and varied career. I really don't think Dr. Who would have cast such a large shadow over him when he is clearly a very good character actor - he always looks different in everything he does and he's done so much. I've seen him in the previews for the upcoming new episodes of Heroes - I wonder what he'll be like!

I don't know if there's a soundtrack to Torchwood or not. I've heard the DVD for only the first half of the season has been released, and only in England - not sure if they released a soundtrack to accompany it. I like the theme, too, as well as the opening scenes. It's been a bit inconsistent in the writing and characterization, but I think that's fairly typical of any first season as everyone (writers, dirctors, actors, etc.) is getting to know their jobs. I'm looking forward to a second season, because I think they're looking at some really interesting stuff, delving a bit deeper into more fascets of humans than Dr. Who does.

First up, though, we get another season of Dr. Who with David Tennant, his third - makes me wonder how long he'll stay!

how i spent my friday

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hyperbolic plane crochet

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