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Ramanujan and a Formula for 1/Pi


Date: 04/06/98 at 23:13:41
From: JOHN XENAKIS
Subject: Pi

This is for my production and operational management class at Rutgers.
Who is the man with infinity, and what is his formula for Pi to the
17,000,000th place?


Date: 04/08/98 at 10:17:46
From: Doctor Lester
Subject: Re: Pi

"The Man Who Knew Infinity" is the Indian mathematician Srinivasa 
Ramanujan (1887-1920), and that description of him is the name of a 
book about him (written by R. Kanigel), but I do not know who first 
gave him that title.

Ramanujan was entirely self-taught, and discovered many important 
results for himself. He is described as 'The Man Who Knew Infinity' 
for the intuition he had for the subject.

He was eventually 'discovered' by the rest of the world, and he was 
invited to Trinity College of the University of Cambridge (in 
England!). His colleagues there included the mathematician Hardy, who 
recorded the following story, highlighting Ramanujan's talents.

Hardy went to visit Ramanujan in hospital, and said that he had 
arrived in a taxi with the 'dull number 1729'. Without hesitation, 
Ramanujan remarked that the number was in fact interesting, because it 
was the least number that can be written as the sum of two squares in 
two different ways: 1729 = 1^3 + 12^3 = 9^3 + 10^3.

I don't know if this is a true story, or if Hardy made it up (perhaps 
Ramanujan told some flattering tales about Hardy in return)!

Unfortunately, I have been unable to find the formula for Pi that you 
mentioned. But I believe that he came up with an infinite sum that 
equals 1/Pi (as a limit if you were to evaluate all the terms). So the 
formula to 17 million decimal places could involve evaluating the 
first few thousand terms of this series. I remember that even just a 
few terms gave 1/Pi to quite a high degree of accuracy.

I will keep looking for this formula, and mail you again if I can find 
it. You might be able to find out more about Ramanujan on the 
Internet. He is certainly mentioned at the mathematical history Web 
site 

   http://www-groups.dcs.st-and.ac.uk/~history/index.html   

and you could search for other sites on the Math Forum.

-Doctor Lester, The Math Forum


Date: 04/08/98 at 15:16:45
From: AJAX464
Subject: Re: Pi

Thank you for your help. I will check out the web site for his 
formula.
    
Associated Topics:
High School History/Biography
Middle School History/Biography
Middle School Pi

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