Happy Pi Day… April 3?

Going off topic today!

Today is the “Pi Day” of the century, when the calendar reads 3/14/15 and the clock reads 9:26:53 am. We are supposed to be super excited about this because, after all, pi = 3.141592653…

Perhaps I’m just contrarian by nature, but I am not planning to bake a pie or join in any of the other Pi Day festivities. I do love the idea of a math holiday, but … numerology is not mathematics.

The thing that bugs me about Pi Day as a mathematician is that 3.141592653… is only the representation of pi in *base 10*. There is no reason to prefer this to other bases. It’s only important to us because we have 10 fingers. The most natural base for computers is base 2, where pi = 11.00100100001111… Then there’s base 3, where pi = 10.010211012222… And base 4, where pi = 3.0210033312222… Perhaps the coolest base for pi is base 16, because a formula was discovered a few years ago (by Borwein, Borwein and Plouffe) that allows us to compute any hexadecimal (base-16) digit of pi, say the billionth digit, without computing all the previous ones. There is no known formula that allows us to do this for base 10. The hexadecimal notation for pi is pi = 3.243F6A8885A3… By continuing to privilege base 10, we are discriminating against computers and polydactylic people!

My second objection to Pi Day is that it’s not even consistent. We aren’t using base 10. The first digit in 3/14/15 refers to a month, which is computed in base 12. The second digit refers to a day of the month, which is computed in base… uh… 30? 31? Depends on what month you’re talking about. The year, thank goodness, is base 10. But then we get to the clock time 9:26:53, where the numbers are computed in bases 24, 60 and 60 respectively. This isn’t mathematically meaningful, it’s a complete joke.

When *should* we celebrate Pi Day? Well, I would suggest that we do it when the year is pi months old. I think that is kinda sorta what the inventors of Pi Day had in mind. So the first question, obviously, is which version of a month should we use? Sidereal? Synodic? Tropical? Anomalistic? Draconic? I’m voting for the synodic month, 29.530588853… days. This definition of the month is the period from new moon to new moon, which is culturally the most meaningful. Also, this month is comparable to what most people think of as a month; the other ones are all in the 27-day range.

So pi synodic months, calculated to 11 decimal places, is 92.773080996… days. We will reach that landmark on April 3 at 6:33:14 pm. So… go on and celebrate today, if you must. But I will be eating my pie on April 3!

Addendum for math-y friends: I can’t resist adding this puzzle that I already posted on my Facebook page.

Recall that 1 astronomical unit is the distance between the earth and sun. Assume the earth’s orbit is circular, and assume that we define a month as exactly 1/12 of a year. Question: How many months does it take the earth to travel (1 + 1/4 + 1/9 + 1/16 + …) astronomical units in its orbit? (A piece of pie for the first person who answers correctly.)