Thursday, March 17, 2011

Mathematical Constant Day

Celebrating "Pi Day" on March 14 seems pretty arbitrary, to say nothing of lame. When are you supposed to observe "e Day" or "Phi Day"? If you're going to pick a point during the year to recognize pi, why not the moment between January 1 and December 31 proportional to a circle's diameter's ratio to its circumference? This will fall on April 26 most years, and I suppose should be called "One Over Pi Day." (Alas, I see this has all been covered.)

On Pi Day, someone must observe that "The first 144 digits of pi add up to 666." What are the chances that a randomly generated series of consecutive digits will at some point add up to 666 (or any other large, evil number)?

3 comments:

Steve said...

By "any other large, evil number" I mean that we want the value that the chances converge toward as the target number gets larger. For low target values, like 7 and 13, the chances differ because of the limited number of patterns in the first few digits.

We can discover a lower bound by envisoning a worst case scenario. As we get close to the target number, suppose our random digit generator gets stuck and produces only 9s, minimizing the chance of hitting the target. Then we will hit the target one out of nine times, over 11%.

RWH said...

http://vihart.com/blog/pi-is-still-wrong/

Steve said...

Vi makes an entertaining case, but the manifesto convinced me.