## Monday, March 12, 2012

### Pi Day

Wednesday this week, March 14, is Pi Day, as the first digits of $\pi$ are 3.14.  A better approximation of $\pi$ will occur on Pi Day 2016, when 3.14.16 is close to $\pi=3.1415926535$...  Or better yet, at 1:59:27 (am or pm) on March 14, we'll get 3.14 1:59:27.   An even better approximation is on Pi Day 2015 at 9:26:54 (3.14.15 9:26:54).  Unfortunately April only has 30 days, as otherwise people in countries where they write dates in the format dd/mm can celebrate April 31 (31.4) as Pi Day.

There are other variants of Pi Day.  For instance, today March 12 is Pi Day in base 9 ($\pi_{base 9} = 3.1241881...$).
Pi Day in base 3 is October 1 ($\pi_{base 3} = 10.010211...$).
Pi Day in base 4 is March 2 ($\pi_{base 4} = 3.021003...$).
Pi Day in hexadecimal is March 24 ($\pi_{base 16} = 3.243f6...$).

In this manner, many days in March are Pi Day in some number base.

$n$ $\pi$ in base $n$ Pi Day in base $n$
4 $3.021003331...$March 2
5 $3.032322143...$March 3
6 $3.050330051...$March 5
7 $3.066365143...$March 6 (or March 7 after rounding)
8 $3.110375524...$March 11
9 $3.124188124...$March 12
10 $3.141592653...$March 14
11 $3.161507028...$March 16
12 $3.184809493...$March 18
15 $3.21cd1dc46...$March 21 (or March 22 after rounding)
16 $3.243f6a888...$March 24
17 $3.26fag579e...$March 26 (or March 27 after rounding)
18 $3.29fdeh0g7...$March 29 (or March 30 after rounding)