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Nerd crochet - hyperbolic manifold

Harvestar

By Harvestar
in Other Crochet

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Harvestar Enthusiast

Harvestar

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When I saw the "Taking Crochet to a Higher Plane" in the Fall Interweave Knits Crochet magazine, it was what made me buy it.

 

So my first project from it was the n=4 hyperbolic plane. :D

 

My friends (all fellow nerds) think it's cool too.

 

DSCN4424-sm.JPG

 

Now I'm starting to think about what else I could crochet. I do know of someone who did a cross-stitch of a famous Hubble Space Telescope picture.

 

I have always wanted to make stuffed, cute versions of the planets. That wouldn't be too hard, I would think.

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crochettreasures Enthusiast

crochettreasures

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What do you do with a hyperbolic plane? I saw this in the magazine as well. Talk about being a nerd - I actually have the full blown out instructions from the teacher who is using this in the classroom. Its a white paper, but darned if I could figure out the mathematical formulas lol.

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Jewels Enthusiast

Jewels

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I LOVE it!! I just bought the magazine tonight and was excited to see the article. I work with mathematicians so it'll be fun to bring the mag in and pass around the article. I wonder if I can crochet this at my desk since it is "work related"!! Will be cool to make for a new office decoration too.

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shan Newbie

shan

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Is this what happens when you put free time, a passion for physics/maths, and really bright yarn together ? I love the look, but Im not so sure what to use it for. . . maybe a cat wrap. Have you tried Fibonacci sequencing for stripes in your projects yet ? ( ie might be nice way to do THE RINGS around jupiter) Kee3p on creating & just ignore the non nerds out there ( they just dont understand . . . )

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Harvestar Enthusiast

Harvestar

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As for what to *do* with it, I think it will be nice as a demonstration piece in classes. While I'm not in mathematics, astronomers do use hyperbolic planes to describe what an open universe might be like. I really like using 3D models of things.

 

As a bit of an explanation:

 

There are different types of surfaces (think back to geometry here a bit) - there's the flat plane (or Euclidean plane) - this is the surfaces most of us deal with every day - your table, your desk. A straight line is the shortest distance between 2 points. (in geometry terms, a triangle would have all the angles add up to 180 degrees)

 

Then there's a sphere (like, say, the Earth!). In our towns (i.e. small distances) the shortest distance is still a straight line, but if we were to fly from one continent to another, the shortest distance would actually be part of a circle (look at the routes that planes fly across the upper Atlantic the next time you look at one of those in-flight magazines). (also, on a sphere, a triangle would have angles that add up to *more* than 180 degrees)

 

On the hyperbolic plane (just a different type of surface), it's curvature is different - the kind of best way to describe it is to say that a triangle would have angles that add up to less than 180 degrees. Since we don't deal all that often in our own lives with hyperbolic planes, making the model is helpful in explaining this concept to classes. :)

 

(anyone else, feel free to correct or add anything! :) )

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notaknitter Newbie

notaknitter

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try these:

 

Lorenz manifold

finished:

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image18.html

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image17.html

mounted:

http://cerebro.cs.xu.edu/~smbelcas/mclorcay.jpg

http://cerebro.cs.xu.edu/~smbelcas/mclordisp.jpg

 

find it here

http://www.enm.bris.ac.uk/anm/preprints/2004r03.html

 

A variegated hyperbolic plane:

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image15.html

Intructions are in 'Experiencing Geometry'

http://www.math.cornell.edu/%7Ehenderson/ExpGeom/

 

 

Pattern for fractal shawl

http://www.livejournal.com/community/crochet/9822.html

 

 

crocheted Sierpinski blanket

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image11.html

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image12.html

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image13.html

Instructions here:

http://www.math.ucsd.edu/%7Edwildstr/crochet/

 

 

Steiner's Roman surface (and other surfaces)

http://www.math.le.ac.uk/people/cirving/home.html

intructions for making topological surfaces

http://www.math.le.ac.uk/people/cirving/knitting.html

 

crocheted Menger's Sponge

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image6.html

skeletons of platonic solids

http://cerebro.cs.xu.edu/~smbelcas/mkexh2005/mkexh2005-Pages/Image5.html

as far as patterns are concerned, how about Fibonacci

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

 

More hyperbolic planes

http://www.npr.org/templates/story/story.php?storyId=4531695

http://www.theiff.org/oexhibits/oe1e.html

http://www.cabinetmagazine.org/issues/16/crocheting.php

 

 

 

See ya, and good louck

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reecie Enthusiast

reecie

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i agreee!!! :manyheart:yay however, i do know what they are...and am going to make one, just to have around!

 

 

 

 

NERD!!! NERRRRRD!!

 

heh heh...i dont understand physics/math at ALL...so im just gonna sit back here and call ya a NERD!!!:devil

 

just kidding. whatever it is that you made,:D it looks interesting!

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Pyogazel Enthusiast

Pyogazel

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Is this what happens when you put free time, a passion for physics/maths, and really bright yarn together ? I love the look, but Im not so sure what to use it for. . . maybe a cat wrap. Have you tried Fibonacci sequencing for stripes in your projects yet ? ( ie might be nice way to do THE RINGS around jupiter) Kee3p on creating & just ignore the non nerds out there ( they just dont understand . . . )
Well, you can use them as decorations for a Xmas tree, or it can be the trim of a collar or cuffs, and if you crochet around a long chain (instead of a disc) with this formula you can end up with a quite cool scarf ;)
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  • 3 months later...
jimbo Proficient

jimbo

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In-dang-credible stuff in this thread!!!

It made me wonder if anyone has tried, oh, say that impossible triangle that MC Escher has in some of his art work... or birds transmogrifying into fish and so on?

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don't look now Rookie

don't look now

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I got a 24 on my Math ACTs and I'm still completely lost. :lol I was never very good with the difficult stuff (which is why I took Math of Money my last year of high school to complete my math credits and never figured out what an Euler circuit was in college before my teacher kicked me out of that class).

 

I sort of understand what that is, so... it looks cool. Heh.

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Dejhia Explorer

Dejhia

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I made one for my dad (who used to teach math at the Naval Acadmeny) and one for a knitting friend of mine who was a math major in college. They love them. My dad keeps his on his desk at work.....

The knitter I know is going to make all of her ruffles as H.Planes....

 

THanks for all of the links... I will have to check it all out.

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