Today is known as Pi Day in America, because the date (3/14/15) matches the first five digits of pi (3.1415...). Some people have even gone so far as to say that 9:26:53 AM/PM is even more worthy of celebration because that contains the first 10 digits of pi. A mathematician might say that there was a moment in time in which the time was pi itself (that is, sometime between 9:26 and 9:27 AM/PM, there was a time which was pi AM/PM).
I want to propose a couple things:
(1) That the idea of pi day is terribly American-centric. Many countries write the date not as MM/DD/YY (03/14/15) but as DD/MM/YY (14/03/15) -- so the idea that the date matches the first 5 digits of pi is a bit wonky.
(2) In effect, every day is pi day because every date and time because every date and time conceivable will appear in the digits of pi. Given that pi is an irrational number, pi is both never-ending and never-repeating. Thus, every combination of numbers you want (let's say, for example, March 15 at 11:05 AM -- or, in the non-American method of writing, 15/03/15 11:05 = 153151105) will appear at least once in pi ("The string 153141105 occurs at position 151419383. This string occurs 1 times in the first 200M digits of Pi" --according to http://www.angio.net/pi/). We can try to find the same string of numbers in other irrational numbers (say, the square root of 2, for example). Yes, the string might not start at the beginning, but any string of numbers is contained within pi.
Just a couple more pointers:
(3) There is a point in pi where the number 9 appears six times in a row (at position 762: ...11349999998372...). This is called the Feynman point. Just a fun little pattern.
(4) I have heard it argued that the existence of irrational numbers, such as pi, is evidence for the fact that we do not live in a computer-simulated world (we don't live in a Matrix). To contain an infinite number of digits (as we have not yet found the end of pi) means that a computer would require an infinite amount of memory/data processing to store the number pi in its hardware, which, as far as we can tell, is not possible.
Excuse the long delay in between posts -- I've been quite busy.