Last year marked the dawn of a new era in mathematical holidays. Spearheaded by Dr. Michael Hartl, Tau Day (celebrated today, June 28th) is an attempt to draw awareness to what he sees as a fundamental error in the definition of the beloved circle constant . In particular, he (and others) argue that the more natural choice of the circle constant should be , which he affectionately dubs . I outlined the reasons for this in a post last year, though if you have the time, I highly encourage you to read Hartl’s Tau Manifesto.

This year, I thought it would be nice to talk with Dr. Hartl in more detail about his inspirations for Tau Day, and where he envisions it in the future. He was gracious enough to agree to a brief interview, which I humbly submit to you here.

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**Q: When did you first discover that was “wrong”? Did you have an intuition that something was amiss before reading Bob Palais’s 2001 article in The Mathematical Intelligencer?**

A: I don’t remember how deep my suspicions about ran before I encountered that article, but “ Is Wrong!” definitely opened my eyes, and every section of The Tau Manifesto owes it a debt of gratitude.

**Q: What inspired you to write your own manifesto on the subject?**

**Q: What has the response been like to your manifesto? In general, would you say people have been supportive, or are pi devotees too large in number?**

A: Support has been overwhelmingly positive. I monitor Twitter mentions of Tau Day, and nearly every commenter has something nice to say.

**Q: What is your ultimate goal with this project? Would you like to see tau replace pi in textbooks? Would it be enough for students to be exposed to tau concurrently with pi when they learn trigonometry? Given that pi is such an ingrained part of mathematics education, do you have any thoughts on how best to steer this massive ship towards a new definition of the circle constant, especially for students who are first being exposed to trigonometry?**

A: As a social hack of geek culture, the project has already exceeded my expectations. At technical conferences, people often recognize me as “that tau guy”. That said, the problem with pi is real, and I do believe that adding tau to the elementary curriculum would make mathematics more intuitive and more fun. Since the installed base of pi users is so big, the only hope from my perspective is a grassroots effort, which based on reader feedback does seem to be happening. Someday, perhaps the American Mathematical Society and its foreign equivalents will get their act together and we can have a top-down effort as well, but for now it’s bottom-up all the way.

**Q: Besides this debate over the circle constant, are there any other anachronisms in math and science education that you feel ought to be addressed (for example, something along the lines of Ben Franklin’s choice for the sign of electric charge, which you mention in your manifesto)? Aside from the mathematics itself, what can students learn from these discussions over which choices are more natural than others?**

A: Fixing the sign of electric charge (in short, electrons, not protons, should be positive) is virtually impossible, since all the old textbooks would have to be rewritten. In contrast, switching from pi to tau can happen incrementally. There are some other anachronisms, but I’m not sure they’re worth fixing. (The temperature scale, for instance, is subtly broken, but what we have is probably good enough.)

Students can learn from this subject that notation matters, and that even geniuses (e.g., Euler) sometimes make mistakes. They can also learn that just because (nearly) everyone believes something, that doesn’t make it true.

**Q: A big contributing factor to Pi Day’s success has undoubtedly been the food. Besides eating twice as much pie, do you have any ideas on how to build Tau Day into a distinct mathematical holiday?**

A: Tau Day happens during the summer, so perhaps we could add a distinctive outdoor component. Tau Day at the beach? I’m certainly open to suggestions!

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Though I’m usually a curmudgeon when it comes to mathematical holidays, Tau Day does present a somewhat unique educational opportunity, and since it is still new to the scene, there is ample opportunity for people to contribute to future traditions. It is in this spirit that I offer the following suggestion for today (and future Tau days!):

1. Embrace the season.

I agree with Dr. Hartl here. Kids are out of school, and this might seem to put Tau Day at a distinct disadvantage. On the other hand, a summertime holiday naturally lends itself to outdoor activities (at least in this hemisphere). Since tau is all about relating the circumference of a circle to its radius, there are many ways to explore this relationship in an outdoor setting. If you’re celebrating at the beach, you could have a circle drawing contest, where each contestant is given a line in the sand and tries to draw a perfect circle with the given line as its radius. The circle for which the ratio of circumference to radius is closest to tau would be declared the winner. Or, if you are celebrating by a lake, you could attempt to measure the circumference of the lake, and use it to determine the size of a circle with equal circumference. Planned carefully enough, one could hint at the isoperimetric inequality (though perhaps not too explicitly, depending on how excited your kids are to do math during the summer). Any activity involving some kind of perimeter measurement could work here.

2. Cut the memorization.

As my readers know, I am no big fan of the recitation contests that have somehow become a Pi Day tradition, in which people compete to see how many digits of pi they can recite. Reasons for my objection can be found here. Given that pi and tau are so closely related, it might be tempting to introduce a similar contest for Tau Day. But these contests offer little in the way of actual mathematical learning, and are terrible PR for mathematics in general. In order to help Tau Day mature into its own independent entity, I would advocate for removal of any recitation contests. If the focus is on a mathematical constant, let’s focus on some real mathematical insights – this would be more educational, and could be more fun too.

What would these activities look like? There’s plenty of freedom here. If you have kids interested in computers, one of my readers wrote up some Tau Day activities related to formal proof writing and machine automated proof verification. There is some cool stuff here, though sitting for too long in front of the computer may run counter to the first suggestion. Whatever you decide, the purpose should be to emphasize mathematics as a creative pursuit full of ideas, not one that relies solely on blind memorization.

3. Take the food to the next level.

Non-math students who enjoy Pi Day probably enjoy it for the food. If we are to hook people on Tau Day, food will probably remain an important component. But if you advocate that tau should take the throne from pi, then it seems only natural that the food on Tau Day needs to be cranked up to 11.

As tau is nothing more than two times pi, pie still remains a natural food choice – simply make twice as much. I think we can do better, though. One idea: the Tau Day Pumpple.

The Pumpple consists of two pies – one pumpkin, and one apple. This takes care of the pun. To really take it to the next level, though, the two pies are then baked inside of a cake. I can think of no better way to celebrate.

Now, given that it is the summertime, perhaps a pumpkin pie isn’t entirely appropriate. With so much fruit in season, one has tremendous choice in selecting a dessert appropriate for today’s festivities. One could bake a Chapple, perhaps (cherry and apple), or maybe even a Bleach (blackberry and peach). As long as two pies are baked inside of a cake, the spirit of the holiday will be honored.

Any other suggestions for Tau Day festivities? This has the potential to be the only math holiday I’d willingly support, so I hope some truly exceptional traditions take root.

(Thanks to Michael Hartl for taking the time to answer some questions, and to Jim for the Wikiproofs link!)

I’m reminded that there are two useful parameterizations of the exponential distribution, one with mean lambda, and one with mean 1/lambda.

Well, you could go to Wikiproofs using a tablet computer while on the beach. Just trying to help…

My own observance was at a pie store where we each had two slices of pie and sat on circular stools. The woman behind the counter had heard of pi day but had not heard of tau day until I told her about it.

@Jim – True enough. Ah, the wonders of 21st century living!

Hi again, Matt. I was thinking about pi day coming up next month, then I remembered Vi Hart’s video http://www.youtube.com/watch?v=jG7vhMMXagQ and wonder if you’ve seen it. (Vi’s pretty badass cool in all mathematical doodling!) Cheers!

Hi Fawn,

Yes! I have seen the video, although fairly recently (I hadn’t seen it the last time pi day rolled around). I agree with you, her doodling is pretty fantastic.