Friday, September 25, 2009

D.I.Y. Disorienting Holiday Gift Ideas for the Mathematically Inclined

Above, we see a baby Felix Klein and the Klein bottle which was later named after him. Baby Felix's German family probably didn't give him lots of useless presents around the holidays, and he turned out okay (aka brilliant mathematician/physicist). All of this going out an buying extravagant gifts for the holidays just strikes me as silly, and the Holiday Sales are already starting, trying to entice all of us poor people to dish out dollars for useless junk. So I thought I'd start a list of math-themed gifts under $15 that are sure to please. Everyone knows that mathematicians love to be disoriented -- or at least they know that being disoriented is nothing to be ashamed of.

Make a Glass Klein Bottle for your favorite mathematician:
Don't remember what a Klein Bottle is? Take a cylinder and glue the ends together with opposite orientation. In other words, as you traverse clockwise around one end, glue the other end counterclockwise. Can't do it? That's because it can't be done in three dimensions without letting the cylinder intersect with itself. Acme Klein Bottles is a company that specializes in beautiful glass Klein Bottles that are, in general, pretty expensive. BUT, the good news is Acme Klein Bottles, there is a $10 option that may appeal to those conservationists/penny-pinchers among you.
The Jigsaw Puzzle comes with a free band-aid!

Make a Mobius Music Box for your loved one:

I ordered my very own DIY Music Box Kit, and made my own little music box! It was fun and you can do it too.
Take a gander at Think Geek's Kit.
AND Note that you can punch your own holes to compose an original backwards\upside down masterpiece.
By the way, August Mobius is the namesake of this strip, which was also discovered by a man whose last name was Listing. But which sounds cooler "Listing" or "Mobius"? Yeah, that's what I thought.

I have not tried this next one, but judging from my minimal knitting skillz, I may stick to the "Mobius Scarf", which I saw at Oiyi's Crafts Blog.

Make a Klein Bottle Hat to keep those precious brains warm:
Mathematician Sarah-Marie Belcastro generously provides instructions at her website for knitting these self-intersecting representations of the Klein Bottle. There is also a link to making hyperbolic baby pants.

Really, Real Projective Space deserves more recognition here. I mean, it's disorienting too!
In case you don't remember real projective space, it is what you get by taking a sphere and identifying (gluing together) antipodal points (i.e. the north and south pole). Since this space cannot be embedded (made accurately) in three dimensions (try it), we will make do with "Boy's Surface", which is an immersion (has self-intersection) just as our models of the Klein Bottle are. This immersion was part of Werner Boy's 1901 Thesis written under the Famous Mathematician Hilbert. The surface, which is pictured above, was discovered as a result of Hilbert's request for Boy to prove that no such immersion existed. So, even famous guys can be wrong!

Make Your Boy (or Girl) Boy's Surface:
Courtesy of Joe Field's website, you can use just good old fashioned paper, scissors, and tape to make Boy's Surface.

Lastly, I make the observation that all of these unorientable manifolds were first described by Germans -- coincidence?
Yeah, Probably. But a funny one!

Okay, I'd love to see some other disorienting and inexpensive gift ideas from my readership, which I imagine to be growing exponentially -- as in from 0 to 1 maybe :)

Monday, September 14, 2009

Game and Movie of the day


Want to kill some time doing a little group theory in disguise?
Check out the game Expacon designed by Dr. Gilbert Baumslag of City College of New York. The name of the game comes from the "Expansion/contraction" of words allowed by the rules. If you ever took group theory, you will recognize this as a thinly disguised exercise in showing that certain words written in the generators of a group are trivial. If you don't know what group theory is, you will have some fun!
Also, there is an upcoming conference October 1st and 2nd in New York on the subject of finitely presented groups, the first part of which is designed with graduate students in mind.


Like Origami and Mathematics?
Basically, as Robert Lang points out in his recent TED talk, folding up enormous sheet-like objects into small packages is a skill that is in demand in many scientific communities. The provocatively titled new movie "Between the Folds" which features (among others) Robert Lang and mathematician Tom Hull explores connections between the art of paper folding and the sciences. The film will be shown on PBS on December 22.

Friday, September 11, 2009

The Mobius Music Box!

Back in February 2009, artist Ranjit Bhatnagar decided to make an instrument a day as part of a course he was teaching at the Parsons School of Design in New York, and one of those days he was inspired to create a Mobius Music Box which plays a song forwards AND backwards as many times as you can turn the crank!

Here is a link to his blog Moonmilk

Wednesday, September 9, 2009

Alice Munro Writes about Sonja Kovalevsky

Just wanted to bring attention to a new short story by Alice Munro, a famous Canadian short story writer, about the mathematician Sofia Kovalevsky. In only 41 years, this amazing mathematician managed to accomplish a lifetime's worth of goals. Unlike many stories about mathematicians, Too Much Happiness paints a picture of a sane, amiable, and relatable mathematician while relating some of the challenges faced by a pioneer. Check out the short story in the July Harper's Magazine or in her new book of short stories of the name Too Much Happiness.
Just a note, the stamp shown was created in her honor by her country during the same time that she was refused any job there. Can you imagine someone who could get their face on a stamp but couldn't find a job?

And here's a great joke I heard that has nothing to do with Sonja Kovalevsky, but which, given her interest in writing (she completed several novels), I'd like to think she might have appreciated:

"What's longer: mile or kilometer?"

The answer of course is kilometer because if you remove mile from kilometer, you are left with something .... "koter".

Unfortunately I did not make this up. I read it in a thread in which the answer to the question in quotes was, believe it or not, hotly debated!