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Madhava's π
Centuries before Newton, Kerala's Madhava summed an infinite series to find π.
Worked demonstration
Madhava of Sangamagrama (Kerala, c. 1400) found π/4 = 1 − 1/3 + 1/5 − 1/7 + … — odd denominators with alternating signs. What is the denominator of the 19th term in this series?
Try it yourself
Why it works
π/4 = 1 − 1/3 + 1/5 − 1/7 + … : the denominators are the odd numbers, the nth being 2n − 1, with alternating signs.
Background & Explore Further
Madhava of Sangamagrama (c. 1340–1425) developed genuine pre-Newton infinite-series analysis and computed π to ~11 decimals. Explore the Kerala school and the Yuktibhasa, often called the first 'calculus' text.