Pi. Pi is not just a number. Its much more than that. For ages, it has intrigued mathematicians.My interest in it started when I, with two of my schoolmates in our junior classes, learnt that the world famous, and notorious: 22/7 is not the correct value of Pi. Then what actually is ? And how much correct that is ? Our quest inspired us a lot to find ways of calculating the 'EXACT' value of Pi, which unfortunately, was impossible to find.
At that innocent age, first way that came to our minds was to draw a very very (and very :) ) big circle by some means at some place, measure the circumference, and the diameter. Just divide the circumference by the diameter, and what we have is a much closer approximation of it. The idea was good - but HIGHLY IMPRACTICAL ...:)
Thinking hard and getting nothing ... we went to our maths teacher 'Dr. Pankaj Gelda', whose image in our minds was not less than a Galileo. He told us - "I have three or four expansions for Pi. I'll bring them for you." Expansions for Pi ? At that age, we knew that terms like sin(x) and cos(x) can have expansions, but how come a constant has an Expansion !! "Yes, we can have"- he told. "Put x=1 in the expansion for Tan-1(x)". Voila!! We were all set to make our first computer program for calculating what we thought would be the most correct value of Pi in the world !! (Ignorant minds are happy !! :) )
But, there was a problem....
(To be continued...)