Talk:False position method

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated C-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
C Class
Low Importance
 Field: Discrete mathematics

Removal dd 4 Febraury 2005[edit]

I removed the text because I found it impossible to justify. Calculus is not needed to arrive at the idea of secant lines. The linear problems mentioned in the Nine Chapters do not use secant lines; in fact, I would argue they do not use the false position method either but linear interpolation. Finally, I could not find any evidence in History of calculus and Moscow and Rhind Mathematical Papyri that the Egyptians developed calculus, except for the false statement that one needs calculus to calculate the volume of a frustum. -- Jitse Niesen 18:18, 4 Feb 2005 (UTC)

Egyptian mathematics[edit]

To the editor with IP address Could you please explain (or give references explaining) how the ancient Egyptians used the false position method? The example in Egyptian mathematics suggests that given an equation ax = b, they try one value, say y, compute ay and compare the result with b to get the solution. I am trying to understand the differences with the method of double false position as used by the Chinese. Thanks, Jitse Niesen 10:24, 4 Apr 2005 (UTC)

Rule of False Position?[edit]

How does the method described in this article fit in with the "method of false position" described at [1] and [2]? Do we need to say something here about other uses of the terminology? Tom Harrison Talk 20:53, 6 May 2006 (UTC)

Yes, it should be mentioned, perhaps via a disambiguation page. I think that the methods are related, but the rule of false position described on the web pages you mention is considerably less sophisticated. I haven't found a good reference on this though. -- Jitse Niesen (talk) 12:15, 7 May 2006 (UTC)
Another external link for when the Rule of False Position page is created: *Rule of False Position at Convergence --Nic bor 18:23, 3 July 2007 (UTC)
False position as used in Ancient Egypt is described in sources such as
* Clagett, Marshall Ancient Egyptian Science, A Source Book. Volume Three: Ancient Egyptian Mathematics (Memoirs of the American Philosophical Society) American Philosophical Society. 1999 ISBN 978-0871692320
* Katz, Victor J. (editor),Imhausen, Annette The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press. 2007 ISBN 978-0691114859
* Gillings, Richard J., Mathematics in the Time of the Pharaohs, Dover Publications, 1982 reprint (1972) ISBN 0-486-24315X
From their description the method of false position (also called false assumption) as used in Ancient Egypt is not iterative. It really does not follow the general outline of the technique from numerical analysis as outlined on this article. I have only seen examples where the method is used to solve linear and simple quadratic equations. It may be a very simple version of the modern technique, but I really like Jitse Niesen's suggestion that this method be given it's own page and that this one links to it via disambiguation. I will probably write something up over the weekend (time permitting). Regards --AnnekeBart (talk) 13:34, 9 October 2010 (UTC)

different visualisation[edit]

Visualisation of the false position method.

is anyone interested in integrating this into the article? i find it looks a bit nicer than the old one... —The preceding unsigned comment was added by (talkcontribs) 17:06, 31 May 2006 (UTC) It is "do it yourself" around here. Why not add it yourself, if you think that it is good. But I would not remove the old diagram, if I were you. JRSpriggs 04:52, 1 June 2006 (UTC) P.S. You should give copyright information (who created it and confirmation that he/she gave permission) even for diagrams posted on talk pages like this one.

Division vs. multiplication[edit]

Regarding the example code: since the compiler will convert the floating-point division by a constant into a floating-point multiplication by the (precomputed) reciprocal of that constant at compile time, there is no need to make the code less clear in order to gain speed: the machine code generated will be the same in either case. -- The Anome 12:05, 11 January 2007 (UTC)

Even faster than multiplying by one half, is shifting one bit to the right. Which optimization the compiler will also do for us, if it is any good (and knows what the constant is). More important still is that the code should be clear to the reader. JRSpriggs 05:35, 12 January 2007 (UTC)
Since only variables with the type double is divided by 2 in the C code, it would wreak havoc on the result to shift it in order to achieve a division by two. Shifting is only equivelant to division and multiplication (depending on the direction of the shift) when dealing with integers -- never floats. —Preceding unsigned comment added by (talk) 03:35, 15 January 2009 (UTC)

error in equation?[edit]

in the last equation, : f(b_k) + \frac{f(b_k)-f(a_k)}{b_k-a_k} (c_k-b_k) = 0.

shouldn't c_k and <b_k></math> be switched like this?

 f(b_k) + \frac{f(b_k)-f(a_k)}{b_k-a_k} (b_k-c_k) = 0. —Preceding unsigned comment added by Ceazare (talkcontribs) 20:37, 18 March 2010 (UTC)

Difference Between False Position And Bi-Section Method for Finding real roots[edit]

Difference Between False Position And Bi-Section Method for Finding real roots —Preceding unsigned comment added by Ankurpatel12 (talkcontribs) 06:52, 6 June 2010 (UTC)

false what?[edit]

It would be helpful if the article could explain why the method bears such a poetic title. Tkuvho (talk) 14:46, 3 March 2011 (UTC)

Bad method?[edit]

In the section "Illinois algorithm" it says: "While it is a misunderstanding to think that the method of false position is a good method, it is equally a mistake to think that it is unsalvageable." This statement seems subjective and not appropriate for an encyclopedia. Usually one compares one method to another and points out pros and cons objectively. The author should at least elaborate why he/she considers this method so bad. Italo Tasso (talk) 21:32, 8 March 2012 (UTC)

Indian mathematics[edit]

On 19 March 2006, Deeptrivia added this sentence: "The oldest surviving documents demonstrating knowledge and proficiency in the false position method is the Indian mathematical text Vaychali Ganit..." (since then, the spelling was changed from Vaychali to Vaishali). No source for this statement was provided at the time, nor has any been supplied since that date. The statement needs to be reliably sourced, or else it should be removed. Rks22 (talk) 00:12, 9 June 2012 (UTC)

Double False position method originated in China, spread to Europe via the middle east and then returned to China via the Jesuits[edit]

Dun, Liu, 2002. "A Homecoming Stranger: Footsteps of the Double-False-Position Method." In: From China to Paris. 2000 Years Transmission of Mathematical Ideas. Edited by Yvonne Dold-Samplonius, Joseph W. Dauben, Menso Folkerts & Benno van Dalen. Stuttgart: Steiner. [Abstract: Appearing first in the Nine Chapters on Mathematical Procedures (ca. 50 AD), the Double-False-Position Method spread from China into Central Asia in the Middle Ages and became known as the "Khitan algorithm" [hisâb al-khata'ayn] among Arabic mathematicians. Leonardo Fibonacci (1170?-1250) devoted a separate chapter to this method in his Liber Abaci (1202). When the Jesuits introduced Western mathematical knowledge into China in the early 17th century, they claimed that the Double-False-Position Method was a new technique invented by Western mathematicians and could not be found in the "old text" of the Nine Chapters. This is because ancient Chinese mathematical books had become extremely rare at that time. Therefore when the Double-False-Position Method appeared in the Tongwen suanzhi (1613) and Xijinglu (ca. 1610), it was said that "a stranger came from overseas"].

07:47, 8 February 2014 (UTC)