http://unimodular.net/blog/?p=116 ecstatic over numbers Thu, 09 Sep 2010 16:01:51 +0000 http://wordpress.org/?v=2.5 http://unimodular.net/blog/?p=116#comment-13891 carlos Sat, 03 Jan 2009 19:46:25 +0000 http://unimodular.net/blog/?p=116#comment-13891 There's a great article in a recent Scientific American by Jonathan Borwein and Peter Borwein on "Ramanujan and Pi." The series is written in different form, as [tex] \frac{\sqrt{8}}{9801} \sum_{n=0}^{\infty} \frac{(4n)!(1103 26,390n)}{(n!)396^{4n}} = \frac{1}{\pi} [/tex]. Each new term betters [tex] \frac{1}{\pi} [/tex] by about eight digits. This development in 1914 was a HUGE improvement over Gergory's (1671) arctangent-of-1-equals-pi-over-four series expansion, convergence to a any reasonable approximation requiring hundres of terms. Machin's (1706) arctangent expansion was better, but nothing like Ramanujan's. There’s a great article in a recent Scientific American by Jonathan Borwein and Peter Borwein on “Ramanujan and Pi.” The series is written in different form, as . Each new term betters by about eight digits. This development in 1914 was a HUGE improvement over Gergory’s (1671) arctangent-of-1-equals-pi-over-four series expansion, convergence to a any reasonable approximation requiring hundres of terms. Machin’s (1706) arctangent expansion was better, but nothing like Ramanujan’s.

]]> http://unimodular.net/blog/?p=116#comment-12631 tpc Tue, 23 Sep 2008 00:53:42 +0000 http://unimodular.net/blog/?p=116#comment-12631 Dear Manjula, I don't know your background but I presume you are from India from your email. To achieve something in maths, you have to start learning it somewhere. A good place would be a university. Best wishes. Dear Manjula, I don’t know your background but I presume you are from India from your email. To achieve something in maths, you have to start learning it somewhere. A good place would be a university. Best wishes.

]]> http://unimodular.net/blog/?p=116#comment-12598 manjula Sun, 21 Sep 2008 06:13:49 +0000 http://unimodular.net/blog/?p=116#comment-12598 i love maths & ramanujan i watnt to do some think in maths but no one support me plz give feed back to me i want to achive sometink in maths i love maths & ramanujan i watnt to do some think in maths but no one support me plz give feed back to me i want to achive sometink in maths

]]> http://unimodular.net/blog/?p=116#comment-10363 annalise Tue, 04 Mar 2008 17:41:35 +0000 http://unimodular.net/blog/?p=116#comment-10363 high school musical is the best move high school musical is the best move

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