Monday, April 30, 2012

Hyperbolic Felt Lace Bracelets

My new friends and I met for our second "Make Stuff Sunday" yesterday, and we continued to play with felt.  As you can see from my last few posts, I devised a technique for making chunky felted lace which can be used to make surfaces of all types, and I've been playing around with it to see what is possible.
In this post, all of the (lone) pieces in the photos are examples of hyperbolic surfaces, meaning they have saddle points or negative curvature.  Informally, it's a saddle point if the concavity goes up in one direction and down in another direction.  One super cool fact about hyperbolic surfaces is that the geometry on a hyperbolic surface fails the parallel postulate, which is why I think everybody's been calling it a postulate for so long and not an axiom.... but I digress.  In terms of sewing, you might say that a piece of hyperbolic fabric has ruffles, or it flares like you get when you add gussets to a skirt.  This is in contrast to flat fabric (i.e., normal fabric) or something that curls into a ball, like the blue-purple bracelet here...
...or the green-purple bracelet on the bottom of this photo.  The top bracelet is hyperbolic, and the bottom bracelet is spherical with positive curvature (i.e., it's a ball).  I like the way you can stack them into a vase.
This purple and black piece resembles a hyperboloid, but I checked it for straight lines and it failed to have them.  So it's still hyperbolic, but a little too ruffled to be a true hyperboloid.
This is a little crown for a snow queen.  I stitched beads to the felt to look like snowy ice crystals. Like most crowns, this piece flairs out at the top, thereby making it hyperbolic.  It's more or less the same size as the others, and it still fits as a bracelet, but I intended it mostly to be worn on top of the head as a crown.   I think it would look nice with a wedding dress, something blue, and all.
This cute little ruffle isn't a bracelet, but it is an awesome little hyperbolic surface.  More precisely, it's a patch of the hyperbolic tiling by pentagons, where four pentagons meet at every vertex.  It's called the order-4 pentagonal tiling.  This piece was created by mathematical rock star, Vi Hart (she calls herself a mathemusician, but I kind of like mathematical rock star).  After our adventures last week making Seifert surfaces in felt, Vi wanted to felt a hyperbolic tiling.  I gave her some instructions to get her started, and she did everything else.  
In fact, it was her expressed desire to make this piece that led me to devise this technique for felted lace.  This is a nice example of how representing abstract mathematical objects as sculptures leads to more general techniques.  I really love it when that happens.  Math inspires art, which then gives me a reason to write about both.  
The yellow is wool, and the orange is recycled sari silk, which Vi used to emphasize the boundary.  After playing with hers, I kind of want one.   But I also want to make a felted hypercube.  Too many choices...

18 comments:

  1. Gwen - these are fabulous! I want to live the rest of my life at the intersection of art and math - especially if you keep turning out such beautiful examples of it.

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    1. Thank you ladies. (Ladies? I'll just assume so until I hear otherwise...) I'm glad you like them. See, math is fun! No, really :)

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  2. Love the shapes, colors and wearability.
    Greetings,
    -Eva Maria

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    1. Thank you, Eva. These bracelets are remarkably comfortable and wearable, especially considering how large they are. I'm tempted to keep them for myself, but alas, no...

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  3. Great stuff Gwen. I love the purple and green "vase" of cuffs :)

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  4. This is absolutely gorgeous! Are you shaping the felt on a form to get the shape, or is it just the shapes you're using to begin with? I have only done nuno felting once, so I'm only just getting my feet (or wool...) wet with the art/craft.

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    1. Dawn, yes, I'm using a form to help me organize the holes, but sizing these bracelets has proven to be very elusive. I want to write a tutorial explaining precisely how I make these, but I'm still working on my technique. I'll explain it all in the tutorial at some point, as soon as I figure out the method to my madness. Thanks for your comments.

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  5. Lovely blog with so many interesting and inspiring posts! Love your work:) Would you like to follow each other?

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    1. Sure thing, Laura. I just signed up to follow your blog. Thanks!

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  6. Hello,

    I am very impressed with your work, specifically the yellow hyperbolic bracelet. Would mind please to elaborate more on how you made it? Thank you!

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    1. The yellow one isn't a bracelet. It's just a toy. You turn wool roving into felt with water and agitation.

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  7. Hello,
    I am very impressed with your work, especially the last yellow bracelet. Could you please elaborate more on how you made it?
    Thank you!

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    1. Wool roving turns to felt with water and agitation.

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    2. But if you don't mind me asking, how did you achieve the hyperbolic form?

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    3. I don't mind you asking but that doesn't mean I'll tell you how I did it.

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    4. I'm an design researcher and I've been developing architectural objects inspired by natural forms (specifically hyperbolic forms) for almost a year now, I'm sorry to have bothered you by asking to exchange knowledge of this. Nevertheless, thank you for your very kind reply and help.

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    5. Like I said, I don't mind that you asked. Have you shared any of the work you've been doing with hyperbolic forms on the internet somewhere?

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