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Keeping it Real: An Addendum

Last week, Dan Meyer invited the folks at Mathalicious to opine on the meaning of the phrase “real-world,” not as it applies to MTV shows (though that would make for a great conversation), but as it applies to questions asked of students in a math classroom. This week, we responded, continuing what I believe to be an important and interesting discussion about the nature of what we mean when we demand that mathematics be made more “real” for our students.

Most of my thoughts on the subject are encapsulated in the Mathalicious response. (Both articles come highly recommended, and what I say below may not make much sense if you haven’t read them first.) The conversation got me thinking, though, and so I’d like to offer my own personal aside/addendum.

When I began writing in this corner of the internet in the summer of 2008, my goal was simply to talk about mathematical ideas in a way that was accessible for a general audience (and in particular, an audience that didn’t necessarily think...

It's Not Complicated. Or is it?

Though I am hardly AT&T’s biggest fan, I can’t help but be charmed by their “It’s Not Complicated” ad campaign.  Each ad features a dapper looking man asking softball questions to a group of young children.  Though the ads are meant to elicit mostly meaningless platitudes that AT&T then spins as selling points (e.g. “Faster is Better”), the children’s answers and the gentleman’s reactions make the ad-watching experience just a little bit more bearable.

In one of the campaign’s more recent ads, however, I was disappointed to see a teachable moment go to waste.  I suppose this is what happens when you have a cell phone company spokesman in a room full of children instead of an actual teacher.  (Though to be fair, the math involved isn’t really suitable for elementary school.)

Here’s the ad:

In case you don’t have time to watch cell phone commercials, here’s a transcript of their conversation.

AT&T Guy: What’s the biggest number you can think of?

Girl 1: A trillion billion zillion...

Down with Plurality!

Hi friends,

As some of you may know, in general I don’t hold our country’s voting methods in very high regard.  Think about the way we vote for president, for instance.  Aside from not asking voters to state any preferences at all, it’s difficult to do worse than our current system: we can only show our support for a single candidate, when in fact our preferences may be more nuanced.  Moreover, since we can only vote for a single candidate, there’s little incentive to vote for our favorite one, unless our favorite happens to be a front-runner.  This is known all across the universe, as evidenced by the Presidential runs of Kang and Kodos:

Even worse, a third party candidate who garners a decent amount of support may end up hurting his own party and parties more closely aligned to it by acting as a “spoiler.”  Of course, the most well-known example of this is Ralph Nader, who many people believe cost Al Gore the 2000 election (for more on the spoiler effect, see here).

For all these...

Mathalicious Post: Most Expensive. Collectibles. Ever.

Hey y'all.  My most recent post on the Mathalicious blog has been live for a while, but in case you missed it, I’d encourage you to go check it out!  Consider it a Simpsons themed cautionary tale for collectors on a budget.  Here’s a sample:

One of the more recent trends in the world of Simpsons memorabilia is the advent of the Mini-Figure collections, produced by Kidrobot.  Each series (there have been two so far) consists of around 25 small Simpsons figures, each with his or her own accessories.  The figures cost around $10 each ($9.95, to be precise), so an avid collector would need to spend something like $250 to complete each of the two collections, right?

Well, not quite.  When you buy one of these figures, you have no idea which one you’ll get, because the box containing the figure doesn’t indicate what’s inside.  All you know are the probabilities for each figure, and even those are sometimes missing…

Given this information, here’s a natural question: how many of these boxes...

Math in Books: The Universe in Zero Words

I recently had the pleasure of reading The Universe in Zero Words: The Story of Mathematics as Told through Equations.  Written by Dr. Dana Mackenzie, the book frames mathematical history in terms of some of the most important equations ever discovered.  While writing about equations for a general audience can be a dangerous game, Dr. Mackenzie tackles mathematical notation head on.  If the sight of an equation causes a chill to run down your spine, fear not; the book eases you in with the very simplest of equations (we’re talking 1 + 1 = 2 here) and guides you gently through a history of mathematics, from antiquity to present day.

Of course, as you move closer to the present, the equations get a little more sophisticated.  Even so, Dr. Mackenzie does his best to ground the equations to something relatable to a wide audience (and by and large, he’s quite successful).  For instance, he uses whales as a way to talk about non-Euclidean geometry: you can read more about this example

Mathalicious Post: Doubling Down

My latest entry on the Mathalicious blog riffs on the strategy of doubling down, using the film Swingers as a jumping off point.  Here’s a preview:

“You always double down on 11, baby.”  Sage advice from Vince Vaughn’s character in the 1996 film Swingers.  At one point in the film, Trent (played by Vaughn) and Mike (played by Jon Favreau) make an impromptu trip to Las Vegas, and Mike ends up completely out of his depths at a high-stakes blackjack table…Mike receives a six and a five, giving him a total of eleven.  Trent urges him to double down, and indeed, this seems like good advice.  After all, in a deck of 52 cards, 16 of them have a value of 10 – that’s over 30%!  Always doubling down on eleven is also consistent with the basic blackjack strategy popularized by Edward O. Thorp in his book Beat the Dealer.  From a mathematical standpoint, Trent is right.  You should always double down on eleven.
Interested in the rest of the story?  Click here!

Mathalicious Post: To Foul Or Not To Foul

Greetings, mathletes. As some of you know, I’ve recently joined the crew of good folks at Mathalicious. Consequently, the blog work here is in a bit of a transition, but don’t worry! I will still be around, though the focus may shift somewhat.

How Math Goes Pop! will be changing is the subject for another post. One thing’s for sure, though: I’ll be contributing to the Mathalicious blog regularly. My first post, on whether or not it makes sense to foul the opposing team at the buzzer in a close basketball game, went live last week. Here’s a small sample:

A three point shot by Sundiata Gaines turned a two-point loss for the Jazz into a one-point win. No doubt that’s a tough defeat for Cavs fans and players alike, but in such a situation, there’s really nothing the defense could’ve done to change the outcome.

Or is there? What if, instead of letting Gaines take the shot, the defense had fouled him? Could that have increased the Cavs’ likelihood of maintaining their lead? If Gaines...

Pi(e) Mathematics

Gentle reader, I apologize for the dearth of updates recently. But with a new month comes new opportunity for mathematical investigation, so let’s dive right in!

In keeping with my summertime theme of mathematics and food (see e.g. here and here), I’d like to share with you a story about a recent dinner I shared with my better half. After a day spent apartment hunting, we decided to treat ourselves to a dinner out.

Everything we learned about treating ourselves we learned from Parks and Recreation.

In keeping with the theme of treating ourselves, we ordered two desserts at the end of the night, and both looked quite delicious. We agreed to each eat half of one dessert and then trade for the second half.  One was in the general pie family of desserts.

Given a slice of pie, the most natural way to divide it in half is to bisect the angle formed at the end of the slice.


One slice of pie, cut in half by bisecting the green angle.

To cut a slice of pie in this manner, one generally...

Asking the right questions

If you read about math and enjoy the internet, chances are you saw this op-ed in the New York Times over the weekend.  The piece, titled “Is Algebra Necessary?,” argues that math requirements, algebra in particular, are prohibitively difficult for many people, and may be contributing to high school and college dropout rates.  Instead of imposing an algebra restriction, author Andrew Hacker suggests restructuring the curriculum around “citizen statistics” and “quantitative reasoning."  Despite the jargon-y names, he insists courses like this could be developed without sacrificing rigor or dumbing down the curriculum.

As might be expected, the piece has furrowed quite a few brows.  A few friends have asked me for my opinion, but I’m a little late to the game, and there are a number of people who have expressed my views in their own words quite well.  I’ll briefly add my own to cents, peppered with links throughout.

First, I agree with Dan Meyer that the question "Is Algebra Necessary...

Hot Dog Mathematics (a.k.a. Hot Dog! Mathematics!) Part 2

Last week we talked about hot dogs.  Though I spent most of my time discussing how the dog’s surface area changes if it is cut lengthwise (also known as a butterfly cut), my original inspiration came from much more sophisticated wiener slicing.  Around the fourth of July, the following video went viral.  Take a look; it’s hard not to see the merits of this suggested technique for cooking hot dogs.

As the curly fry is to the regular fry, so too is the spiral cut dog to the regular dog.  Indeed, it’s hard to find a reason why one should not choose a spiral cut dog over a regular dog, if given the choice.  But from a mathematical standpoint, as with the butterfly cut discussed last time, arguably the most interesting feature of the spiral cut hot dog is the increased surface area.  Unlike the butterfly cut dog, however, computing how the surface area changes when dealing with a spiral cut dog is not so straightforward. In particular, it is difficult to compute the additional surface...

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