This year’s theme is mathematics and sports, a topic which has inspired a number of articles . . . → Read More: Mathematics Awareness Month 2010]]> As April comes and goes, so too does Mathematics Awareness Month.  Every year, the Joint Policy Board for Mathematics swirls mathematics with a different delightful discipline: last year it was climate, and the year before was voting.

This year’s theme is mathematics and sports, a topic which has inspired a number of articles here on this site.  As usual, there are a number of essays that discuss this theme from various perspectives; while usual suspects such as football and baseball play a central role in many of the essays, other sports get to mingle with mathematics as well, including track, golf, and tennis (also NASCAR, if you consider that a sport).

This dude always thinks about math when he is golfing.

There are too many articles to discuss, so I’d encourage you to go take a look and see if anything strikes your fancy.  However, here are a few highlights:

If football is your game, Chris Jones of St. Mary’s College of California has written an article about NFL overtime rules and offers a mathematical model for determining the winner in overtime based on the winner of the coin toss at the beginning of overtime.  Since overtime ends after any team scores, one would naturally expect that winning the coin toss carries with it a significant advantage, and this is born out in the data.  Jones offers an alternative rule scheme whereby the winning team is the first one to score six points, but in this case the team which wins the coin toss still has an advantage, and it is more likely that the game will end in a tie.

Given that the NFL recently changed their overtime rules for playoff games, it’s too bad that Jones did not include this scheme into his analysis.  Perhaps, gentle reader, this would be a good exercise for you.

If your sports preferences are more varied, you may prefer the article by Rick Cleary of Bentley University, which discusses the probability of rare events in the contexts of football, baseball, and basketball.  My favorite example deals with the complaints many people have with regards to playoffs in Major League Baseball.  More specifically, the first round in MLB playoffs pits teams into a best-of-5 series, while the remaining rounds of the playoffs use a best-of-7 series.  Critics claim that the shorter first round series puts the stronger teams at a disadvantage, but in fact, a 7-series round is only slightly more advantageous for the stronger team.  In effect, Cleary argues that it’s almost incompatible to say that a best-of-5 series is unfair without also arguing that a best-of-7 series is also unfair.  The article is also well suited for a general audience.

Then again, maybe you are more interested in the intricate links between math and golf.  If that’s the case, you may want to peruse this article by Scott M. Berry, in which he analyzes the question: is Tiger Woods a winner?  In other words, does his ability to win transcend his skill level?  Does he have a mental game that helps push him to the top because of the influence he has on other players?

Berry modeled Tiger Woods’ performance with the affectionately named RoboTiger, and concluded that in fact, Woods’ record does not prove him to be a “winner” – he’s just a very skilled golfer. The jury is still out, however, on the mathematical significance of any “winning” label for Tiger woods in the bedroom.

Finally, if you’re interested in turning mathematics into cash, you may be interested in this article by Tim Chartier, Erich Kreutzer, Amy Langville, and Kathryn Pedings, which discusses different methods of predicting winners in the annual NCAA Men’s Basketball Tournament.  While I’ve discussed this topic before, this article gives more detail on a variety of methods, which, if carefully applied, will make your bracket a sure fire winner.  Just make sure no one else in your local pool is so mathematically inclined.

There are plenty of other examples illustrating the intersection of math and sports, so don’t let the magic stop here.  If you’ve ever wanted to learn how to bend it like Beckham, or if you’ve ever dreamed of somehow connecting math to NASCAR, click through to the Mathematics Awareness Month website and read on.

The evidence is fairly compelling. According to this article from sfgate.com, the famous crooner misappropriated Einstein’s famous mass energy . . . → Read More: Mariah Carey Is not a Mathematician]]> This may come as a surprise to some of you, but it has come to my attention that Mariah Carey is not, in fact, a mathematician. Moreover, I’m fairly certain she is not a physicist, either.

The evidence is fairly compelling. According to this article from sfgate.com, the famous crooner misappropriated Einstein’s famous mass energy equivalence formula E = mc²:

In interviews to promote the record, the singer’s eleventh studio release, Carey told reporters she re-interpreted the equation to stand for “emancipation equals Mariah Carey times two.”

Forgetting for a moment the question of what it means for Mariah Carey to be one half of emancipation, there is the arguably more important issue of her not understanding the difference between mc² and mc x 2. Granted, Mariah Carey didn’t get this far based on her math skills, but by botching what many consider to be the most famous equation in mankind’s body of knowledge, it’s hard not to shake your head a little bit.

Perhaps the interviewer caught her off guard, when she was too focused on deeper mathematical questions. Or, perhaps Mariah Carey has defined a new measurement of velocity, called the Mariah, which is equivalent to one half of the speed of light – with these units, of course, the expressions mc² and mc x 2 coincide. Unfortunately, Occam’s razor forces me to confront what is most likely the ugly truth: MC just doesn’t know her math.

“So what?” you may say. “People don’t like her because she’s good at math.” That’s a fair point. And while I enjoy a good laugh at a pop star’s expense just as much as the next guy, what may be even more troubling than her comment are the comments from everyday folks responding to the story, some of whom display a fundamental lack of mathematics knowledge that rivals Carey’s own. For example, we have the following:

Wouldn’t the correct formula then be E=MCx2? Then again, Carey’s job isn’t rocket science.

Where has America’s math education gone? Wherever it is, it certainly isn’t in the realm of pop culture.

Hey Einstein, do you like apples?
Well, Mariah Carey took your formula.
How do you like them apples?

In summary, the Mail Goggles feature allows you to make Gmail aware of certain . . . → Read More: Math as Your Wingman: Mail Goggles]]> As many of you with Gmail accounts may already know, Google launched a feature last week that aims to put arithmetic squarely in the shoes of your most trusted wingman. The feature, dubbed Mail Goggles, is explained in the Official Gmail Blog.

In summary, the Mail Goggles feature allows you to make Gmail aware of certain hours during the week when you should not be sending e-mail (due to exhaustion, inebriation, or the side effects of whatever other illicit things you do in your personal life). Once these hours are set, should you decide to send an e-mail during one of these highlighted times, you will first be prompted to answer a series of math questions, in an attempt to prove to Gmail that you have sufficient mental faculties to be sending e-mail.

A noble pursuit, to be sure. A trustworthy internet wingman may be just the thing for those among us who may enjoy their night life a bit too much, only to make decisions they regret in the morning. And while a wingman tied to your e-mail can’t help talk you down from every form of debauchery, there are certainly situations in which such a feature could be useful.

Unfortunately, Mail Goggles is kind of a fair weather wingman. He’ll check in on you every once in a while, but if you tell him you’re fine, he’ll leave you alone. He might tiptoe around the issue of whether or not you’ve had enough to drink, but talk forcefully enough and he’ll back down. That may sound ok, but sometimes you need a wingman who has the resolve to set boundaries for you when you’re not in a condition to set them yourself. Sadly, Mail Goggles is a bit too much of a pushover.

Maybe Mail Goggles could learn the laws of Wingmandom if it
watched more VH1. Or if it bought a big poofy hat.

I have reached this conclusion after experiencing firsthand what the Mail Goggles system has to offer. Today I went in and warned my e-mail that between the hours of 3 and 4 pm on Wednesdays, I was not to be trusted with the “Send” button. I then attempted to send an e-mail to myself, and sure enough was prompted with a list of math questions.

Now, you can tell Mail Goggles how difficult to make the questions, by setting the difficulty to be a number between 1 and 5, 1 being the easiest, and 5 being, well, the less easiest. Not wanting to peak too soon, I asked for the easiest questions, and so was not surprised when the following problems greeted me:

I was slightly more surprised by the amount of time I had to solve these questions: 60 seconds. With a whopping 12 seconds allotted per question, even someone with minimal computational ability could easily plug and chug these answers through a calculator within the allotted time – and when you’re already at the computer, the thought certainly must be tempting.

And let’s be honest – you’d have to be pretty far gone not to know what 10 + 10 is.

Itching for more of a challenge, I went back into the settings and ratcheted up the difficult to level 5. Ready to get those synapses firing, I tried another test e-mail, and was given the following questions:

For every guy who has dreamed of looking like a Hoobastank concert attendee, or for every girl who has dreamed of looking like a Bratz doll, Yahoo! Answers provides you with a forum to not only construct the avatar of your dreams, but also to ask questions on a variety of topics, and . . . → Read More: An Open Letter to Users of Yahoo! Answers]]> Dear Yahoo! Answers Users,

For every guy who has dreamed of looking like a Hoobastank concert attendee, or for every girl who has dreamed of looking like a Bratz doll, Yahoo! Answers provides you with a forum to not only construct the avatar of your dreams, but also to ask questions on a variety of topics, and get real answers from real people.

She only loved him for his soul patch.

Unfortunately, as a math educator, I feel compelled to offer criticism regarding the Mathematics section of your site. The existence of this section is not what bothers me – it is the user behavior, both of those asking questions and those answering them.

Let’s start with the askers. I’ll be blunt: please stop using the internet as your interactive cheat sheet. There are a number of users of Yahoo!’s service who have no qualms asking for answers on their homework – many do it blatantly, and with no regard to the importance of these formative years in their mathematics education.

Consider the following examples:

Exhibit A: Fractions help please =/ ughh math is so hard!?

The question is as follows:
1.] 2/3-1/2
2.] 1/2-1/8
3.] 9/5-1
4.] 3/4-1/8
5.] 1- 5/9
6.] 6/9 – 1/6
7.] 2/3 + 1/9
8.] 8/9 – 2/3
9.] 1/2 + 1/2

No attempt is made to give any sort of context: what part of these problems is difficult for this individual? Moreover, since these problems are all solved in exactly the same way, it is clear this person is only looking for quick answers to their homework, and not an understanding of how to solve these types of problems.

Exhibit B: Is there a website tht i can type in math problems and will me the answers?

This one is pretty self explanatory.

Of course, these are some of the most obvious offenders, but there are numerous other examples of students (mostly younger ones) abusing the privileges given to them by the folks at Yahoo!.

Needless to say, this is something that should be discouraged. Parents taking a more active role in monitoring their child’s internet habits will help, of course. But it is just as important to change the behavior of those answering the questions, because no matter how obvious it is that you are trying to cheat, somebody will answer you, with no questions asked.

In the case of Exhibit A, as of the time of this writing there are 16 answers to the “question.” Of these, 8 give answers to all nine parts of the question, and of those 8, 3 give answers without showing any work whatsoever (note that giving an answer is not the same as giving a correct answer). My favorite response is provided by a gentleman who chastises the questioner by saying, “It’s not fair to use Yahoo! Answers to solve your maths homeworks,” and then proceeds to write down the answer to every question.

There is only one answer to exhibit B, but sure enough, it is a link to a website that will do all the work typically asked of a middle school student in math. Not a word of reprimand is offered.

We have all heard the old adage praising the benefits of teaching someone to fish, rather than simply giving someone a fish. The people who answer these types of questions, however, don’t just give you the fish: they clean it, cook it, serve it, cut it up into tiny pieces, then chew it for you and spit it into your mouth. All that’s left for you to do is receive the regurgitation, like baby birds. The difference being that baby birds don’t need to know how to add fractions.

The thought of his daughter never learning how to
fish is enough to make this man cringe.

What can be done? While mathematical abuses at all levels of education seem to be occurring on Yahoo! Answers, it is more prevalent with the most basic material, suggesting the most common culprits are the very students who most need to build a mathematical foundation. For more advanced levels or mathematics, I shift the blame more towards the questioner, but for younger students, who may not see what long term harm a lapse in their mathematical understanding can have, the onus moves to those answering the questions, who should know better than to sell out their knowledge for some measly Yahoo! Answers “points” (the purpose of which is still not entirely clear to me).

It is with this in mind that I implore you, Yahoo! Answers users, to stop spoon feeding middle school homework answers to students. You do them a disservice, and by failing them, you are failing our collective future.

I should mention that not all of the mathematics category is corrupted. There are plenty of examples of people asking intelligent questions (questions aimed at understanding material and not just getting the right answer, for instance), and there are also many examples of people answering the questions only partially, but giving full details for the parts they do answer so as to help guide the student’s understanding. This is all well and good. But as long as someone can get answers to their homework without having to think, our work is not complete.

In conclusion, letting the internet do your homework for you is most likely a bad idea. Using the internet to help you understand your homework is, in general, a good idea. So parents, make sure you know whether your child is using the internet for good or for evil. The distinction could cost them an understanding of mathematics – or even their lives.

Well, maybe not their lives. But certainly this behavior should be discouraged.

I thank you in advance for your cooperation.

With lukewarm regards,
Matt

It is with this in mind that . . . → Read More: Designer Math]]> A well designed t-shirt has the power to delight and inspire; it can break the ice at the start of the evening, and seal the deal at the end. It can be a powerful tool for social interaction, and can help forge the bonds that will last a lifetime.

It is with this in mind that I bemoan the present state of mathematically themed t-shirts, many of which are asinine to the point of nausea. I also feel the need to speak out and warn those who would consider buying such t-shirts for friends or loved ones, under the misguided impression that anyone who studies math will appreciate (much less wear) a t-shirt just because it is related to math.

Let’s analyze some examples, to see just what’s gone wrong with the current state of mathematically inspired fashion. The following five designs can be found here, along with a multitude of others. However, every design seems to fall into one of the categories below:

1) The Symbol Design (epitomized by the pi design):

Many t-shirt designs seem to be of the philosophy that by throwing a bunch of math symbols on a white background, somehow their shirt is clever or interesting. In particular, there are a plethora of t-shirts focused on pi, its decimal approximation, or some pun involving pumpkins or actual pies. Pi seems to have become the poster child for mathematics, which I guess is ok, but I think you will be hard pressed to find a single mathematician who will find the transcription of a long decimal expansion of pi interesting. And for those mathematicians who already feel isolated from society, I don’t think wearing a t-shirt with a whole bunch of numbers on it will make them feel better.

I wouldn’t have as much resentment towards this particular letter if it weren’t for the fact that it always seems to be hogging the spotlight. How about a little love for e? Is it too much to ask for some love on behalf of the Euler constant? Although such similarly themed shirts would be just as unappealing, at least we would have some more variety. Perhaps it has something to do with the fact that other constants don’t lend themselves as easily to puns involving baked goods.

2) The “Why Is this on a T-shirt?” Design:

Let’s be honest: nobody is going to be impressed if you have a t-shirt with a whole lot of formulas on it. In fact, some people might be downright scared of such a shirt. And in a case like the one pictured here, why would one want a list of algebra mistakes on a t-shirt? This hardly seems like the most effective place to keep a list of common mistakes. Wouldn’t a notebook be more preferable? Not to mention the fact that while wearing the t-shirt, it would be difficult for one to read these examples; the fact that there seems to be no attempt at formatting them only compounds the matter. Such examples often make poor use of the t-shirt medium, and would seem to fit much better elsewhere.

3) The Plain Old Not Funny Design:

Come on now. Is this really the best we can do? Not only does this design juxtapose two horribly uninspired slogans, but the pun is terrible. If we’re going to go that route, shouldn’t the shirt say “Math nerd rocks rock!!”? And how can a rock hold a pencil behind its head with no ears?

4) The Minimalist Design:

Sometimes these designs can rise above mediocrity, but I don’t see how they could inspire one to make a purchase. I do appreciate the simplicity of the design pictured here – in fact, of the five displayed here, I would consider this particular design my favorite. It does not smack of effort as do so many other designs, but at the same time, it is this very same feature that keeps this type of design from rising above its brethren.

I would, however, highly recommend the thong version of this item, if you are looking for a gift for that someone special.

5) The Math Crutch Design:

Designing a t-shirt based on mathematics can be difficult: on the one hand, you want to make a joke that people who study math will find amusing, but the shirt should also be decipherable to people who do not do math. Otherwise, why should anyone wear such a shirt in public? Presumably, one wears funny t-shirts to project the impression to others that one has a keen sense of humor. But if many people don’t understand your shirt, what then?

This shirt should not be undecipherable to anyone who remembers some basic calculus – unfortunately, asking that of our citizenry seems to be a bit much. On the other hand, one can be thankful that the calculation is not difficult, so that even if your calculus is rusty you should be able to dust off the cobwebs and compute the joke. However, even though this t-shirt does give one that light bulb moment when the content is understood, the punchline itself is a bit crass for general consumption. Certainly, one should hesitate before wearing this shirt to try and get a rise out of a room full of mathematicians, at least if the mathematicians are senior to the wearer.

What then, is a fashionable young mathematician to do? Is there no safe haven from uninspired, math-themed t-shirt designs? I think one will find, upon scouring the internet, that resources are indeed limited. However, there are a few rays of hope that shine brightly through the darkness. Perhaps my favorite example is given by the image below.

This design, from threadless.com, is one I would proudly sport on my own masculine frame. It works because it is not actually a joke about mathematics, but a joke taken from pop culture that uses math to deliver the punchline. As such, it becomes accessible to a wide audience, and shows how even rappers can benefit from mathematics. While strong arguments could be made against the plausibility of a linear model as the best fit for the relationship between money and problems, the basic idea is clear, and can be easily understood and admired by people from all walks of life.

Of course, the life of a mathematician can be fraught with disappointments, and this case is no different: the design pictured here has been sold out for such a long time, one wonders if it will ever be restocked. At the same time, one can take solace in the knowledge that somewhere, somebody is looking at this shirt and having a good laugh with mathematics.