Gottfried Leibniz, the 17th century German philosopher and mathematician,
developing a method for calculating pi which, with the hindsignt of history, we can now see had apparently been discovered somehat earlier by the Scottish mathematician and astronomer James Gregory, and also been derived by Madhava, a 14th century mathematician in India.
What is termed the Leibniz formula for computing pi essentially stated that:
π / 4 = 1 - 1/3 +1/5 - 1/7 + 1/9 - ...
This method of computing pi essentially makes use of an "infinite series" which converge on the value of pi, and can be referred to as the "infinite series" method of determining the value of pi.
Although it provides fairly accurate results, it is extremely consumptive of resources - it requires a considerable amount of caluclation before the value even begins to approach pi.
What is notable about this "infinite series" method is that its discovery and use by various individuals marks the transition to a period when the methods for calculating pi became primarily anaytical, as opposed to classically geometric.
