Transcendental PI and its decimals

Imagine for the moment that you can draw a perfect circle. Now divide the circumference of that circle with its diameter. Do you know what number will you get as a result? Of course, it is PI=3.14159... there is no end and no repeating pattern in its decimals, and it is transcendental number. Babylonians believed that it is somewhat bigger than 3, they had approximation 3 and 1/8, 3.125 Egyptians believed it is 4*(8/9)^2. In geometry angle of 180 degrees is equivalent to PI radians.

German matematician Ludolph van Ceulen calculated first 35 decimals of PI. Those decimals are engraved on his tombstone in Leiden. In wikipedia we can read that one English matematician spend 20 years of his life to calculate about seven hudred decimals:


The English amateur mathematician William Shanks, a man of independent means, spent over 20 years calculating pi to 707 decimal places. His routine was as follows: he would calculate new digits all morning; and then he would spend all afternoon checking his morning's work. His work was made possible by the recent invention of the logarithm and its tables by Napier and Briggs. This was the longest expansion of pi until the advent of the electronic digital computer centuries later. In 1944, D. F. Ferguson (with the aid of a mechanical desk calculator) found that Shanks had made a mistake in the 528th decimal place, and that all succeeding digits were fallacious.


Interesting thing is that the first man who calculated one million decimals of PI, with help of computer has the same surname Shanks. It is Dr. Daniel Shanks and his team at the United States Naval Research Laboratory (N.R.L.) near Washington, D.C, and it is said that there is no family connection with William Shanks, despite the same surname.

There is a lot of interesting stuff connected to PI. Cadaeic Cadenza is 1996 short story by Mike Keith (the beginning is by E. Poe), and in its words it has first 3834 digits of PI. Full text of it you can find in this link. Japanese mental health counsellor Akira Haraguchi holds current world record of memorizing PI decimals. He can memorize 83431 PI decimal places. If you wish to calculate huge number of PI decimal places, you can use PiFast program. And if you want to search for string of numbers (perhaps for your birthdate) you can click here, there is a very fast PI online searching method.

Today is 11th February 2006. I'll try to search for string of decimals 11022006 (DDMMYYYY format). There is such string in number PI, after 115,903,340 decimals (115 million hey :)