That remarkable Pi

Google’s Pi Day Doodle.  The Doodle shows Pi in various mathematical settings.  The arrowed item pertains to one of the posts highlighted here.

Wednesday, March 14, is Pi Day.

If you are not familiar with Pi Day, here is the story:  March 14 is called Pi Day because it is 3/14, and of course 3.14 is Pi rounded to two digits (Pi being 3.1415926535897932384626433832795…).  It has been celebrated in various forms for thirty years.  Google did a Pi Day Doodle in 2010.

Pi is fascinating.  It is infinite, but it is not repeating and it is not ‘random’.  It means something—namely the ratio of the circumference of a circle to its diameter.  Within its infinity are many interesting things.  Its infinity of digits contain all sorts of numbers; you can explore what is in the first two billion digits using the SubIdiom Pi calculator (click here for the calculator).  Try it out.  Put in some digits.  See if those digits can be found in the first two billion digits of Pi.

For example, how about the numbers 1-9 in ascending order?  SubIdiom says that the numeric string 123456789 appears at the 523,551,502nd decimal digit of Pi.

Those same numbers in descending order, 9-1?  SubIdiom says that the numeric string 987654321 appears at the 719,473,323rd decimal digit of Pi.

Or 1010101?  The numeric string 1010101 appears at the 15,656,119th decimal digit of Pi.  Here it is in context:
…70115424170555187273101010169014724145321687000…

Interestingly, 101010101 (note the extra 01) is not found in the first two billion digits of Pi.  Maybe it shows up in the next two or ten billion digits.

One wonders whether, if we coded Shakespeare’s play Hamlet into numbers (for example, using A=1, B=2, C=3, etc.) and turned it all into a number, is Hamlet not within Pi?  Is the U.S. Declaration of Independence in there?  The Magna Charta?  The Epistles of Paul?

There is so much within Pi, more than can possibly be comprehended.  Nevertheless, the more we study Pi the more we learn.  And yet, no matter how much we learn, our knowledge will always be negligible compared to what is there to know.  And where did this Pi come from, anyway?  Why does Pi exist and why is Pi, Pi?

Check out the following Pi posts from previous years:

Pi Day and 2 Pi

Homemade Pi (Part I)

Homemade Pi (Part II)

According to Scientific American and the University of Chicago Research Computing Center, Christoph Grienberger calculated Pi out to forty digits—3.141592653589793238462643383279502884197—the most digits to ever be worked out by hand. He published this value in his Elementa Trigonometrica of 1630. And, pertinent to this Vatican Observatory blog, Grienberger was a Jesuit astronomer at the Collegio Romano (the V.O. is home to many Jesuit astronomers).