It would seem that I am not alone . . . → Read More: Happy Tau Day?]]> In the past, I’ve used this blog as a platform to make clear my mixed feelings about Pi Day, a math themed holiday celebrated every year on March 14th (3/14, har har) in honor of the beloved mathematical constant .  My thoughts on the subject can be found here.

It would seem that I am not alone in my frustration.  Michael Hartl, an educator and entrepreneur (as well as a Ph.D. graduate from Caltech), has just today launched a website in favor of Tau Day as a replacement for Pi Day.  However, his argument (based on a 2001 paper by Bob Palais) goes a step farther – he argues that day shouldn’t be celebrated because isn’t the fundamental constant we should be considering!  Rather, he argues that the true fundamental constant is , which is approximately 6.283185… .  Hartl argues that this should be the fundamental constant of interest, and renames it (for reasons given on the website).

Why should this be viewed as a more fundamental constant?  Recall how is defined – it is the ratio of a circle’s circumference to its diameter.  But a circle itself is more naturally defined in terms of the radius, i.e. as the set of points whose distance from the center is equal to the radius.  Because of this, doesn’t it seem more natural to consider the ratio of a circle’s circumference to its radius, rather than the ratio of circumference to diameter?  Put another way, isn’t a more natural constant given by the circumference of a circle with radius 1 rather than the circumference of a circle with radius 1/2?  He offers plenty of other aesthetic examples for why should be viewed as more fundamental, including references to the Bernoulli numbers and simple quadratic forms.

On the one hand, this may seem like a trivial issue – after all, the difference between and is only a factor of 2, and different normalizations of quantities are quite common in mathematics.  On the other hand, Hartl does make a convincing argument from a pedagogical point of view.  His strongest argument comes from trigonometry.  When students learn to convert between radians and degrees, they learn that corresponds to full revolution.  From this, one sees that half of a revolution corresponds to an angle of , 1/4 of a revolution corresponds to an angle of , and so on.  But if we define the fundamental quantity to be , then in radians, half a revolution is , a quarter of a revolution is , and the measure of c revolutions is given by for any number c.

Hartl concludes the following: “The unnecessary factors of 2 arising from the use of are annoying enough by themselves, but far more serious is their tendency to cancel when divided by any even number. The absurd results, such as for a quarter circle, obscure the underlying relationship between angle measure and the circle constant. To those who maintain that it “doesn’t matter” whether we use or in teaching trigonometry … from the perspective of a beginner, using instead of is a pedagogical disaster.”

It’s an interesting argument, and one I think students would benefit from seeing.  is fairly entrenched, so I’m not sure how much of a following Hartl will gain, but even if remains the standard, offering students this viewpoint can only help them as they learn trigonometry.  For that reason, I for one will be endorsing Tau Day (6/28, get it?).  It certainly doesn’t sound as delicious as Pi Day, and the fact that students are out of school is a bit of a problem, but today is apparently the inaugural Tau Day, and these are wrinkles that I’m sure can be ironed out.

So happy Tau Day to you, no matter your preference!

(Big ups to James Hawkins for sending me the Tau Day link.)

Aside from the mathematical arguments one can make . . . → Read More: e day?]]> If you come here regularly, you know of my complaints regarding so-called “math holidays” that get plenty of press, but rarely have anything to do with actual mathematics. The most well known is pi day, celebrated here in the states on March 14th, also known here as 3/14.

Aside from the mathematical arguments one can make for or against this holiday, there is a larger problem. It’s all well and good to celebrate pi day on the date representing the first three digits of pi, but this is only possible if we write dates in the MM/DD format. Most of the world, however, uses the (more logical) DD/MM format, therefore depriving them of such a delicious play on numbers.  Many loyal international fans of this holiday no doubt decry the fact that April has only 30 days, for otherwise they could simply celebrate pi day on 31/4. As it is, they are left with two options: Celebrate on 3/14 like those of us in the states, or enjoy a neutered version of this play on numbers by celebrating on 3/1.

Today I would like to propose an alternative to those for whom the DD/MM notation is standard. Rather than trying to work with imperfect solutions to the pi day problem, take a different number and celebrate it in your own way: the number e.

While e may not be as popular as its irrational sibling pi, it is no less important. No doubt many would argue that it is more important. It is certainly not as well-known in popular discourse, and so highlighting it, I would argue, is more important than highlighting the attention-whore known as pi.  Moreover, since the decimal expansion of e begins with 2.71828183…, countries that use the DD/MM format could celebrate e day today, January 27th.  Sadly, since February does not have 71 days, and since there are not 27 months in a year, people in America would be unable to celebrate in quite the same way – but given all the press that pi day has received over the past few years, I think that’s fair.

Of course, in order to celebrate the holiday properly, one needs activities.  Topics could include the ways in which this fantastic number arises naturally, or a discussion of exponential growth (and orders of magnitude in general).  One could also prove that e is irrational, a fact which follows quite easily from the Taylor series expansion of the exponential function e^x at x = 1.  Perhaps I’m being overly optimistic though – such a holiday would probably include less exciting activities, such as a recitation of the decimal expansion of e to a certain number of digits (a mind numbing activity which is practiced without fail every pi day).

Special consideration needs to be given to a replacement for the act of eating pie, which seems like a suitable activity to do on pi day, but not on e day (especially since the surfaces of pies are circular).  I’m not sure what natural analogue exists – there is one thing that comes to mind when one wants to celebrate a day called “e day,” but I don’t want to promote drug use.  Perhaps instead one could eat foods that start with the letter e, like eclairs, eggplants, and elephants.  But these foods don’t work on a higher level, in that they don’t really relate to the number e in the way that the circular shape of a pie can be related to the number pi itself.

Eggs for e day?

There are obstacles to overcome, that much is certain.  But if we’re going to celebrate holidays related to math, we may as well do a halfway decent job of it.  So happy e day to you – don’t do anything I wouldn’t do.

In fact, I would argue that 09/08/09 is much more interesting. This claim has nothing to do with numerology, and everything to do with President Obama’s speech to the youth of America on the . . . → Read More: Make Money Money, Make Money Money Money! (and Learn Math, too)]]> Let me begin by saying that, in response to the question Why is 9/09/09 so special?, my response is simple: it’s not.

In fact, I would argue that 09/08/09 is much more interesting. This claim has nothing to do with numerology, and everything to do with President Obama’s speech to the youth of America on the value of education. The speech made very clear the importance of taking education seriously, and hopefully convinced students that a good education benefits not only themselves, but also society at large. In case you missed the speech, the transcript can be found here.

Although the speech was about education in general, mathematics got a little bit of love too. Here’s one such example:

What you make of your education will decide nothing less than the future of this country. What you’re learning in school today will determine whether we as a nation can meet our greatest challenges in the future.

You’ll need the knowledge and problem-solving skills you learn in science and math to cure diseases like cancer and AIDS, and to develop new energy technologies and protect our environment. You’ll need the insights and critical thinking skills you gain in history and social studies to fight poverty and homelessness, crime and discrimination, and make our nation more fair and more free. You’ll need the creativity and ingenuity you develop in all your classes to build new companies that will create new jobs and boost our economy.

My thoughts on this irritating trend can be found here, here, . . . → Read More: When will this stop?]]> Ok, now it’s just getting annoying. Odd day? Give me a break.

My thoughts on this irritating trend can be found here, here, and here.

There is no doubt that Pi Day is the most prestigious mathematical holiday, but . . . → Read More: Pi Day]]> Hot on the heels of Square Root Day comes Pi Day, a day held in honor of arguably the most famous mathematical constant, π. And like Square Root Day, I am forced to approach this holiday with a certain degree of hesitation.

There is no doubt that Pi Day is the most prestigious mathematical holiday, but this recognition usually only serves to illustrate the sad state of mathematical literacy in this country. For example, one year I remember reading a news article about Pi Day where the author described π as a number whose decimal expansion “was believed to go on forever.” Of course, belief has nothing to do with it – this is a simple consequence of the irrationality of π, a fact which is apparently lost amidst the pie eating hubbub of this holiday.

Unfortunately, this is not an isolated incident – for as much as Pi Day aims to educate people about π, it seems to do just as good a job of showing how little people actually know. Searching Google News for articles on the upcoming holiday, it’s possible to find a number of stories that say a whole lot of garbage. For example, there’s this quote from a Pi Day article on SF Gate:

Pi, as [Pi Day co-organizer Ron] Hipschman noted, is strange because it’s both an irrational number (its decimal expansion never ends or repeats) and yet the number is also transcendental (no finite sequence of algebraic functions could ever produce it).

To a physicist like Shaw, that kind of contradiction and beauty was all the inspiration he needed to contemplate a Pi Day.

While his heart was certainly in the right place, his mathematical rigor was not. His construction relied upon the unfortunate claim that π = 3.2. Thankfully, the error was pointed out before the bill was able to do any damage. The story does go to show, however, that we have a long history of not understanding π.