| Check
out my Square
Root 2 applet which uses the Bhaskara-Brouckner
algorithm to compute root(2) to any number of decimal places. This
is about the fastest algorithm I have found to do this computation but
if you know different, please email me. I have checked this algorithm
for the first million or so decimal places by comparing it with those
posted at The
NASA Goddard Flight Centre web-site (err not by hand. I wrote
a program to do it!). The algorithm makes
extensive use of Java's BigInteger class. Also try out my PI applet which uses the BPP formula (named after Bailey-Borwein-Plouffe) to compute each hexadecimal digit of PI as a ratio of polynomials. It is a simple matter to convert these to decimal digits. The applet is fairly slow and takes a couple of minutes for 10000 decimal places. I must admit I have only checked this for the first 10000 decimal places. Please email me if you find any errors. Again this uses Java's BigInteger class to do the donkey work. (Does anyone remember that old Star Trek episode where Spock ties up the ship's computer by getting it to compute PI to infinite accuracy thus stopping some alien force taking control?) |