Remember just a few years ago, when there was always the possibility that March 14 could be a slow news day? Then Pi Day could be relied upon to fill some columns on the paper and kill a couple of minutes on the nightly news.
Today, March 14, 2019, is sure to abound with news, a lot of them crazy. But hopefully the newspapers and nightly news will still at least have fleeting mentions of Pi Day today.
As you know, mathematicians use π (the Greek lowercase letter pi) to represent the ratio of a circle’s circumference to its diameter, among other things. This number has a value of approximately 3.14159265358979.
There are people who say we should celebrate Tau Day instead. That would be on June 28.
Some mathematicians use τ (the Greek lowercase letter tau) to represent the ratio of a circle’s circumference to its radius (rather than to its diameter). And of course mathematicians also use τ to mean other things.
In the context of circle geometry, we have τ = 2π, roughly 6.2831853. A consequence of this is that Euler’s identity is then e to the power of i times τ is 1, rather than e to the power of i times π being −1 (and then some people feel the need to add 1 to that in order to get 0 in there, as if −1 was an unimportant number). I personally like Euler’s identity as being equal to −1.
Do we really have to choose to always use only τ or only π for everything? Why not just use one or the other as is more convenient for the situation at hand?
To celebrate π, I now present you with five math non-word problems, all involving the symbol π. The challenge isn’t to figure out the numerical values of these expressions, because I tell you what they are (and they are integers), but to figure out how they mean what they mean. I hope you enjoy these.
You may post the solutions in the comments. Bonus Internet points if you give in your solution how to verify it in Wolfram Alpha or Wolfram Mathematica.