I thought of this Pi Day puzzle yesterday* while getting a haircut. I was thinking about this video by Vi Hart: Many people think that π is special because of its infinite digits. Hart disagrees. Most numbers are irrational like π, with digits that never stop or fully repeat. It is the rational numbers that are in the minority (the infinity of rational numbers is infinitely smaller than the infinity of irrational numbers). Hart doesn’t think π is special for other reasons as well. I disagree. You never know where it might show up. It’s part of the normal distribution formula and “the greatest equation ever”. The infinite digits of π might make it seem weird. But π is a fundamentally important value in mathematics. We forget that its digits also depend on the arbitrary choice of 10 as the base for our number system: “3.1415923…” reflects both the number to be represented (π), and the base (10). This gave me an idea for a puzzle, which I just worked out with a little spreadsheet: What is 30.12120111…? *Today is a “Super Pi Day” in the U.S., since we write the date as 3/14/15, matching the first four digits of π past the decimal. This is only possible once a century. Yesterday was a Friday the 13th. The next Super Pi Day following a Friday the 13th will come in 2415.
CORRECTION, March 15, 2015. The “decimal point” in the puzzle question was in the wrong place. It’s now fixed. Sorry!