## 6 days to Tau Day

22 June 2011

Even now, a select group of mathematicians and mathophiles are counting down to what should (in my opinion) be one of the principal holidays on the mathematician’s calendar.  You’ve all heard of Pi Day, some of you even celebrate it in one way or another (the number of my facebook friends signed up for “The Only Pi Day of Our Lives” surprised me), and it grieves me to say so, but it’s overrated.  At best it should be a minor math holiday.  If you celebrate only one circle-constant-related holiday in a year, it should be Tau Day.  And if you use only one Greek letter as shorthand for a particular constant which is related to circles and mathematically ubiquitous, better that it be $\tau$, the circumference of a circle with unit radius (approximately 6.28318531, which is twice that other number).

Tau Day is 6/28 (by analogy with Pi Day Half Tau Day, 3/14), so our countdown stands at 6 days ($\lfloor \tau\rfloor$ days, if you will).

I won’t get into the details here, but the key contention is that τ, not π, is the circle constant we should focus on.  Instead of $C = 2 \pi r$ (or $C=\pi d$), it would be better to write $C = \tau r$.  For a quick and cute introduction, check out the Pi is Still Wrong video from everybody’s favorite mathemusician, Vi Hart.  For the whole manifesto, check out Michael Hartl’s wonderful site (updated a few months ago for Pi Day Half Tau Day).

Especially for the non-mathematicians here, “should” and “better” might seem strange word choices.  Today I want to focus on what exactly they might mean in this context.

(Remark: If you’re more science-minded, this is a little like the oft-heard-in-some-circles assertion that the convention for positive and negative charges is “backwards”, the opposite of what it “ought to be”.  Apropos xkcd comic!)

## The Two Decks of Cards and the Drunken Hat Check Girl

3 August 2009
1. Imagine you have two decks of playing cards, each thoroughly shuffled.  You give one deck to your friend and keep the other.  Now each of you goes through your deck, one card at a time, flipping cards face up.  You compare your top cards, then you compare your next cards, and so on all through the deck.  If it ever happens that you both reveal the same card at the same time, you win; if you go through the whole deck without such a match, your friend wins.  Who is more likely to win?  You or your friend?
2. Thirty-seven men attend a certain social event and check their hats as they enter.  However, the hat check girl has had a bit too much to drink, and when the time comes to leave, she gives back hats at random, with total disregard for which hat belongs to whom.  What are the chances that nobody ends up with his own hat?