Math Gets Around: Holiday Treats

At this time of year, many people push their studies to the side in favor of roasted animals and pie. However, the activities of enlarging your waistline and mastering some mathematics need not be mutually exclusive. For evidence of this claim, I need only turn your attention to the culmination of thousands of years of human evolution: the Pecan Pie-cosahedron.

Pecans + math = crazy delicious.

This masterful work of craftsmanship was created by an individual known by the pseudonym of turkey tek over at instructables.com. The pie is so named because it has the shape of an icosahedron, arguably the most beautiful of the five1 Platonic Solids (so named because of the Greek philosopher, not because the solids are just good friends). Even better, this isn’t turkey tek’s first foray into mathematically inspired baked goods: also on display is the formiddable Giant Fractal Pecan Pie.

Yes, even pie can be educational.

Such seminal work naturally gives rise to the question: In what other ways can one combine holiday sweets with mathematics? After some careful deliberation, I humbly submit the following ideas.

1) Gingerbread Geodesic Domes.

The gingerbread man leads a tragic life. His sole purpose is to be put on display in the hope that he will be purchased and devoured. Often his life is ended through the horrifying mutilation of his appendages, all in the name of holiday cheer.

It seems reasonable, then, to let the gingerbread man get the most out of his short and sweet existence by accomodating him with a relatively luxurious lifestyle. This is the primary role of the gingerbread house.

While there are many people who pride themselves in their ability to make a fantastic and functional gingerbread house, it is a sad fact that these days, with people looking for quick solutions, boxed gingerbread houses are becoming more and more common. The pieces of the house are all included – all that’s left for the builder is to attach them, so that the process becomes akin to building an edible lego set. Unfortunately, this leads to a certain degree of uniformity in gingerbread dwellings, not to mention questionable quality of the building materials itself.

The least we can do for our small edible acquaintances, it seems to me, is to have enough respect for them that we take the time to build them a unique home, made from fresh gingerbread. With this goal in mind, I believe the gingerbread geodesic dome would be greatly appreciated by gingerbread man and woman alike. Not only would it provide them with a comfortable place to spend their limited time on this earth, but it’s also useful should you wish to provide your gingerbread populace with facilities such as planetariums.

For those interested in learning more about gingerbread geodesic domes, here is an article from Mother Earth News that should provide you with enough information to get started.

This gingerbread family is living large.

2) Sugar Cookie Math Ornaments.

Apparently, in some families it is tradition to decorate the Christmas tree with edible ornaments. The ornaments are made from thin sugar cookies, which are often cut into holiday themed shapes.

However, I see no reason why the holiday motif should be allowed to overshadow equally important themes. Mathematics is always in season, so why not make some cookies that will allow your children to express themselves through mathematics? Let your children decorate the tree with their favorite equality, or let them turn the tree into a center for edible math problems, by allowing them to use the ornaments to pose questions they can then solve! With sugar cookie math ornaments, you can exploit the natural harmony that exists between math and the holidays.

Surprisingly, there’s not much in the way of math inspired cookie cutters, so you may have to do some custom work. You can find some number shaped cookie cutters, and it’s not hard to find Roman alphabet cutters as well. Greek letters, unfortunately, remain elusive.

3) The Dreidel.

This one is easy – the game of dreidel, as with other games of chance, naturally lends itself to many discussions of mathematics. In fact, there are even theorems in math that pertain to dreidels. For example, in 2004, mathematicians Thomas Robinson and Sujith Vijay from Rutgers University proved that the length of a game of dreidel is bounded by a constant times n2 spins, where n is the number of tokens at play in the game.

If you’re looking for a holiday game that incorporates mathematics, you certainly can’t go wrong with a friendly game of dreidel.
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You see, no matter what your plans for the holidays, it’s easy to incorporate mathematics in with your celebrations. Everyone knows that a party can only be made more lively with the inclusion of some math, so whether it’s one of these ideas, or one of your own, don’t be shy about putting giving math an important role this season.
1. For those of you who find it curious that there are only 5 Platonice solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron), here is one elementary proof of this fact.

December 23, 2008 | 1 Comment »

Math in the News: Are Math Teachers Really Only One Chapter Ahead?

It looks like middle school math teachers can’t catch a break. According to a recent study, a significant percentage of math teachers in grades 5-8 do not have a degree or a certification in math. Sadly, the numbers are even worse for schools in low income areas. While it’s certainly true that you don’t need a math degree to teach middle school math effectively, the data does suggest that there is a significant bloc of underqualified math teachers trying to impart essential knowledge to these young students.

Of course, I doubt this is all the teachers’ fault – elementary and middle school teachers are a rare commodity in this country, and kids need someone to teach them math. An understaffed school will do what it takes to make sure there’s somebody at the front of the classroom. And I certainly don’t envy those teachers out there who may not feel so confident in their math ability, but are nevertheless trying to impart all that mathematical know-how because nobody else will.

One thing that is a little confusing is that when this story made the news rounds, most headlines made a statement like: Teachers are only one chapter ahead of their students. The press release for the study, however, makes no such claims – instead, the main point seems to be simply that there are too many teachers without a major or a certificate in the subject they are teaching. This, of course, is an issue that needs to be addressed, but it doesn’t seem to be nearly as dramatic as the headlines would claim. If you’ve taught 6th grade math for five years, even without a certificate or a major, chances are you certainly know the material well enough that you aren’t only one chapter ahead, even if you are a lousy teacher. Similarly, some people have a natural talent for teaching, and can become good math teachers even without much of a mathematical background – just ask The Wire’s Roland Pryzbylewski.

Math teachers in action. You can tell Pryzbylewski means business.
Bottom line: we need more qualified teachers, no doubt. In a perfect world we wouldn’t have to worry about underqualified teachers, because the hiring pool would be large enough to fill schools with the right people. But in the meantime, blaming the teacher for being unqualified fails to get at the heart of our education problems, and so headlines like “Your kid’s teacher is only one chapter ahead!” tend to favor shock value over constructive discussion of the study involved or the problems we face.

Whatever sells papers, I guess.

December 18, 2008 | 2 Comments »

Math in the Movies: Pi

In 1998, Darren Aronofsky shot to success with his independent film, Pi. The film was widely heralded as an excellent film, and earned Mr. Aronofsky the 1998 Directing Award at the Sundance Film Festival. He then went on to direct the similarly successful Requiem for a Dream, followed by the less well-received 2006 film The Fountain. His latest film, the Mickey Rourke vehicle called The Wrestler, opens soon.

The story of Pi centers on a mathematician named Max Cohen, a self professed number theorist – although he never specifies what qualifies him for this title – who spends his days analyzing the stock market and wiping the blood off of his upper lip (I know what you’re thinking, and no, he’s not a cage fighter – that would’ve made the film way better). As he comes closer to “unlocking the secrets” of the stock market (whatever that means), several interested parties begin to come out of the woodwork, all with their own self-interest at heart.

From a math perspective, how does this film stack up? Unfortunately, the answer is poorly. Those wishing to learn some math from their pop culture would be better off with an episode of Sesame Street, or perhaps some School House Rock. In fact, pretty much any math pop culture reference you can think of would probably fare better.

Let’s take a closer look at the stereotypes propagated by this film.

A trailer, for those of you fortunate enough to have not seen this film.
- Mathematicians are really good at calculating things in their heads.

One of our first introductions to Max comes early in the film, when he is leaving his apartment and a young Asian girl approaches him with a calculator. She proceeds to ask him to compute products and quotients of large numbers in his head – things like 421 x 121. Of course, since Max is a mathematician, he has no trouble computing these products. He does it just as quickly as she can type the numbers into her calculator!

As I’ve said before, this isn’t at all a realistic depiction of mathematicians. While there are certainly computational savants amongst us, it is just as common, if not more so, to encounter a mathematician who will willingly admit that he or she is no good at computation. Many mathematicians even take pride in such assertions. Mathematics is as much about doing multiplication in your head as cooking is about opening jars with your bare hands. -1.

- To be successful in math, you have to complete your Ph.D. at an extremely young age.

Max Cohen published his first paper at age 16, and completed his Ph.D. by the time he was 20. While this is certainly not unheard of in academia, the idea that you must be young to be successful is one that is especially pervasive in mathematics.

The problem with this stereotype is that it tends to discourage people from studying mathematics if they are firm in their beliefs that math is solely a young man’s game. In pop culture, most people who are good at math are portrayed as having completed their degrees at a very young age, but in reality these people are the exceptions, not the rules. In mathematics, as Aaliyah will tell you, it is becoming more and more common that age ain’t nothing but a number. -1.

Don’t subscribe to this propaganda: mathematicians enjoy a good samosa just as much as everyone else.

- People who are good at math are socially awkward.

In an early scene, Max is busy looking at numbers on his computer screen (because he’s a number theorist, remember?!) when someone comes knocking on his door. On the other side is his attractive neighbor, who not only sports a British accent, but also has brought him samosas.

Any normal person would welcome such an act with kindness and gratitude. Of course, Max is not a normal person – he is a mathematician. This must explain why he is rude to this woman, both in this scene and later on in the film, despite the fact that she is not only kind to him, but is also cute. That she puts up with his abuse is simply a testament to the power of seduction that comes with studying mathematics, whether intentional or not. -1.

- Number Theory is synonymous with numerology.

Throughout the film, Max stares at numbers. He watches stock prices fluctuate. He prints out random strings of integers from his super old computer and stares at them for long periods of time. Sometimes he even draws circles on the newspaper and shows that he is a genius at math because he can recall the formulas for the circle’s area and circumference.

One notable omission in all of this is that at no point does Max do anything even remotely resembling number theory. If anything, Max’s research would more aptly fall into the realm of financial mathematics, with maybe a splash of ergodic theory thrown into the mix.

At one point Max is so fixated on trying to find a pattern in his work that his mentor, Sol Robeson, tells him, “As soon as you discard scientific rigor, you’re no longer a mathematician; you’re a numerologist.” Coming from a film that depicts nothing BUT numerology, this is somewhat of a surprising statement. -1.

- To be good at math, you must be insane.

Let’s be honest – Max is a total whack job. Not only does he hate it when people deliver him fresh samosas, but he’s obsessive, paranoid (perhaps justifiably so), and irritable. He fantasizes about poking his brains, and at one point he shaves his head and begins drawing on his skull with indelible marker, or so we are led to believe. At least the connotations with phrenology pair nicely with the numerological gobbledygook that permeates the rest of the film.

As I’ve said before (and will no doubt say again), you can be good at math without being crazy. Being crazy is just the frosting on the cake. I kid, I kid. -1.

Wow, look at all the math in that noggin.

- The number π provides an active area of research for mathematicians.

Max’s aforementioned mentor guides Max throughout the film, and often during their discussions, Sol hearkens back to his own youth, and the amazing math he did while researching π.

Sadly, Sol is a century or two late if he expects us to believe he could make a career studying a single number. The whole idea is absurd. I have not heard of a single mathematician who has made a lucrative career studying π, and I think you’d be just as hard pressed to find one. Saying that a mathematician’s research concerns π would be like saying an English literature professor’s research concerns the word “banana.”

The only reasonable conclusion one can draw is that Sol is a fraud. This is further evidenced by the fact that he doesn’t know what density is (weight over volume? Come on, dude). Perhaps Sol was only hanging out with Max to bask in his numerological genius. No doubt his time would’ve been better spent elsewhere. -1.

In summary, this movie scores a whopping -6. This is a pretty poor showing. Sorry, Mr. Aronofsky – if it’s any consolation, I do want to see your new film. Hopefully you are more of an authority on washed up wrestlers than you are on mathematicians.

December 3, 2008 | 1 Comment »