Pi
Posted: Thu Oct 31, 2013 8:03 pm
want to calculate pi manually...........hOw??
Too many ways.
1. On the co-ordinate plane, draw a circle. Find its area by counting the small unit squares that are inside that circle. Now get $\pi$ from the formula $\pi\cdot r^2=$ Area.
2. Buffon's Needle, http://en.wikipedia.org/wiki/Buffon's_needle.
3. Choose two random integers. Check whether they are co-primes. Do this for many times (so many actually) and find out the probability of two randomly chosen integers to be coprime. This is equal to $\dfrac {6}{\pi^2}$.
4. If you have time, sum up some well-known series. Like \[\dfrac \pi 4=1-\dfrac 1 3+\frac 1 5-\cdots\]
And so many. Just use google to find them.