Question

How to calculate the real value of Pi?

Not 22/7 or 3.141 approximations... The original value.

Answer 1

One of the most well known and beautiful ways to calculate Pi (π) is to use the Gregory-Leibniz Series:
π4=1−13+15−17+19−…π4=1−13+15−17+19−…
If you continued this pattern forever you would be able to calculate π4π4exactly and then just multiply it by 4 in order to get ππ.. If however you start to add up the first few terms, you will begin to get an approximation for Pi (π). The problem with the series above is that you need to add up a lot of terms in order to get an accurate approximation of Pi (π). You need to add up more than 300 terms in order to produce Pi (π) accurate to two decimal places!
Another series which converges more quickly is the Nilakantha Series which was developed in the 15th century. Converges more quickly means that you need to work out fewer terms for your answer to become closer to Pi (π) .
Nilakantha Series: π=3+42×3×4−44×5×6+46×7×8−48×9×10+…π=3+42×3×4−44×5×6+46×7×8−48×9×10+…
Mathematicians have also found other more efficient series for calculating Pi (π). Computer programs can add up more and more terms, calculating Pi (π) to extraordinary degrees of accuracy. In 2014 the world record was that a computer has calculated Pi (π) correct to 13,300,000,000,000 decimal places.