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Cuchulainn
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exp(5) = $e^5$

Well, continued fraction were invented by J. Wallis 350 years ago. The link to Ramanujan seems tenuous.How to compute with his method? Does he have a computable solution in a finite number of steps?
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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Jean Piaget

SierpinskyJanitor
Posts: 1069
Joined: March 29th, 2005, 12:55 pm

exp(5) = $e^5$

By all means Sir, no one said Mr. Srinivasa invented Continued Fractions, rather that he has produced outstanding work on these ( amongst many other subjects ). Ramanujan´s notebooks contain many of these proofs, what is striking is that for him, some of these results were not only obvious but also intuitive. Amazing mathematician, one of the Masters indeed. I guess you won´t challenge me on that Dr. Cuch ( broken link btw ). Actually lemme check whether he has produced any Continued Fraction approach to exponentials.
Last edited by SierpinskyJanitor on October 6th, 2011, 10:00 pm, edited 1 time in total.

Cuchulainn
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exp(5) = $e^5$

QuoteBy all means Sir, no one said Mr. Srinivasa invented Continued Fractions, rather that he has produced outstanding work on these ( amongst many other subjects ). Ramanujan´s notebooks contain many of these proofs, what is striking is that for him, some of these results were not only obvious but also intuitive. Amazing mathematician, one of the Masters indeed.I challenge indeed.Amazing guy for sure. But can he compute exp(5) in 5 minutes? if not, then it is N/A. Pure mathematics is *not* Constructive mathematics.QuoteOne aspect of Wallis's mathematical skills has not yet been mentioned, namely his great ability to do mental calculations. He slept badly and often did mental calculations as he lay awake in his bed. One night he calculated in his head the square root of a number with 53 digits. In the morning he dictated the 27-digit square root of the number, still entirely from memory."Numbers my boy, numbers"
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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Jean Piaget

SierpinskyJanitor
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Joined: March 29th, 2005, 12:55 pm

exp(5) = $e^5$

QuotePure mathematics is *not* Constructive mathematics.and who said Pure Maths is all Mr. Ramanujan did? You better brush up on those maths bios Dr. Cuch.

Cuchulainn
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exp(5) = $e^5$

Well, I will stick to Wallis' ALGORITHM for the moment, for many reasons. I am not interested in discussing the history of maths here UNLESS it throws up a algo.////
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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DevonFangs
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Joined: November 9th, 2009, 1:49 pm

exp(5) = $e^5$

QuoteOriginally posted by: SierpinskyJanitorQuotePure mathematics is *not* Constructive mathematics.and who said Pure Maths is all Mr. Ramanujan did? You better brush up on those maths bios Dr. Cuch.Actually I'm quite happy he's brushing up on the QFCL

Cuchulainn
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exp(5) = $e^5$

exp(5) by continued fractions (J. Wallis, 1656).
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Polter
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Joined: April 29th, 2008, 4:55 pm

exp(5) = $e^5$

// We compute the exp(5) using continued fractions.But, do we?

Cuchulainn
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exp(5) = $e^5$

QuoteOriginally posted by: Polter// We compute the exp(5) using continued fractions.But, do we? ;-)Wallis, Maddock, Duffy. A nice check is to do it from scratch.
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Polter
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Joined: April 29th, 2008, 4:55 pm

exp(5) = $e^5$

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Polter// We compute the exp(5) using continued fractions.But, do we? ;-)Wallis, Maddock, Duffy. A nice check is to do it from scratch....because if we do, surely we can remove the #include <cmath> and d = 5.0; cout << "exp " << exp(d) << ", " << endl; will still work?

Cuchulainn
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exp(5) = $e^5$

Quote.because if we do, surely we can remove the #include <cmath> and d = 5.0; cout << "exp " << exp(d) << ", " << endl; will still work? :-)I see. Wanted to test the Boost CF(generator, tol, maxiter) against cmath's exp. yeah: seems compiler is not picking up the exp() I want.. ??
Last edited by Cuchulainn on October 6th, 2011, 10:00 pm, edited 1 time in total.
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Cuchulainn
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exp(5) = $e^5$

QuoteOriginally posted by: outrunHehehe,looks like the -o148 switch injected thatwow! Please elaborate!
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Jean Piaget

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