For many years, I was a skeptic about Pi Day. Calendars seem arbitrary, susceptible to the whim of emperors. Pi seems constant. It is the ratio of the circumference to the diameter for any circle (in the Euclidean plane). A friend sent me a link to a NYTimes article this morning about Pi Day. The article encouraged me to celebrate Pi Day as an opportunity to reflect on the mystery of math in general and π in particular.
Pi Day this year has been made a bigger deal than usual. Drop the 20, go with US date conventions, and we are sitting on 3/14/15: the first digits of π ≈ 3.1415. At 9:26:53 this morning, we had even more digits. Wolfram threw a party in Austin during SXSW. At the time, I was a few blocks away chatting with a gentleman from Scotland over some fresh chalk about an infinite series for π.
The Leibniz formula for π has been attributed to an Indian mathematician at the turn of the 15th century. Madhava is mentioned in the NYTimes article linked above. He arrived at this expression for π from his infinite series for arctan x. Let x = 1, and π/4 results. I took the liberty of multiplying by 4.
For more on π including a look at Archimedes’ work, check out my post from 2013.