The Indian film stars Dev Patel as Srinivasa Ramanujan in ‘The Man who Knew Infinity’. The mathematician used to claim that it was the protective goddess of his family, Namagiri, who showed him in dreams the equations of his formulas. Who is the mathematician in the man who knew Infinity? In the same way that Mozart visualized music, this young Indian had the ability to sprout mathematical formulas with which he tried to explain the world. His case is a spectacular example of how mathematical language is inscribed in the brains of all human beings. Why was Ramanujan captivated by the number pi?Ĭaptivated by the number pi Ramanujan is the icon of mathematical intuition. He calculated π by measuring the diameter of the circle in a remainderless unit and then measuring the circumference in the same unit. More than 4700 years ago, the famous Indian mathematician and astronomer Aryabhatta (b. If the diameter and the circumference of a circle are known, the value of pi will be as π = Circumference/ Diameter. What is the formula for calculating pi? The pi is a ratio and is obtained from a circle. Pi is the 16 th letter of the Greekalphabetand symbolically represented as π and has been introduced to our universe near About 4000 year ago. The first use of mathematics in the Indian subcontinent was in the Indus valleyand dates as far back as 3000BC. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he found a value for the sum of such series using a technique he invented that came to be called Ramanujan summation. Indian mathematicians Madhava and Aryabhata made very significant contributions in finding the exact value of π (pi). In 1987, Chudnovsky brothers discovered the Ramanujan-type formula that converges more rapidly. In 1914, the Indian mathematician Ramanujan discovered the formula for computing Pi that converges rapidly. What Indian mathematician created a formula rapidly calculate the value of pi? 6 Who is the mathematician in the man who knew Infinity?.5 Why was Ramanujan captivated by the number pi?.1 What Indian mathematician created a formula rapidly calculate the value of pi?.As of October 2011, the record was over 10 trillion digits.
USE RAMANUJAN SERIES TO CALCULATE PI UPDATE
Update (18 April 2012): The algorithm used most recently for world record calculations for pi has been the Chudnovsky algorithm. a 16 would be accurate to over 11 billion digits. You can beat this record if you can carry out 16 steps of the method described here. See more here.Īccording to this page, π has been calculated to 6.4 billion digits.
I don’t know whether it has been used more recently. It was used to set world records in 1986. The algorithm given here was state of the art as of 1989. After 10 steps, a 10 is accurate to over 2.8 million digits. To give a few specifics, a 1 is accurate to 9 digits, a 2 is accurate to 41 digits, and a 3 is accurate to 171 digits.
The number of correct digits quadruples at each step because the leading term in the numerator above is 4 n. To see this, note that the number of correct decimal places after the nth step is the negative of the logarithm base 10 of the error: This says that the number of correct digits roughly quadruples after each step. The error in each approximation is given by The terms a n form a sequence of approximations to 1/π.
The following algorithm is based on work of Ramanujan and has been used in several world-record calculations of pi.
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