[math-fun] Indian series for pi
I came across a Math History web site. The authors take seriously the Indian claims of inventing the Gregory series for arctangent, and the power series for sin and cos, circa 1400. http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Madhava.html Madhava's math works are lost, but are described in Nilakantha's writings, including proofs of the series. I suppose the whole thing could be a hoax, but it's a pretty long running one, involving several people. Assuming it's all true, we must ask "What happened to Indian Calculus?" How did it disappear? Why has it only come to Western attention recently? Rich rcs@cs.arizona.edu
I finally got my hands on a paper recommended to me by W. Edwin Clark. George Collins (the author) got it right, but could have simplified more. If b and c are two random integers, then P[GCD[b,c]=1] = (6/Pi^2) If b and c are two random Gaussian integers, then P[GCD[b,c]=1] = (6/Pi^2)/Catalan I think that's a gorgeous result. --Ed Pegg Jr, www.mathpuzzle.com 90m:11165 Collins, George E.(1-OHS-C); Johnson, Jeremy R.(1-OHS-C) The probability of relative primality of Gaussian integers. Symbolic and algebraic computation (Rome, 1988), 252--258, Lecture Notes in Comput. Sci., 358, Springer, Berlin, 1989. 11R27 (11Y40)
participants (2)
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Ed Pegg Jr -
Richard Schroeppel