Talk:Regula falsi

message: I think, the results from "Improved Algorithms of Illinois-Type for the Numerical Solution of Nonlinear Equations", Ford, 1995, should be integrated in the article.
Especially his new methods, which are better than Anderson and Björck, and some of the results from his experiments. Gabriel (talk) 14:00, 25 April 2018 (UTC)
replies: text: WP:Be bold! --Qwfp (talk) 20:15, 25 April 2018 (UTC)
thread_title:  Integrate later results 

message: 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)
thread_title: Removal dd 4 Febraury 2005

message: To the editor with IP address 209.150.67.45: 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)
thread_title: Egyptian mathematics

message: 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 212.117.72.126 (talk • contribs) 17:06, 31 May 2006 (UTC)
replies: text: 212.117.72.126: 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)
thread_title:  different visualisation 

message: 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)
replies: text: 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)
replies: text: 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 77.212.20.61 (talk) 03:35, 15 January 2009 (UTC)
thread_title:  Division vs. multiplication 

message: 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 (talk • contribs) 20:37, 18 March 2010 (UTC)
thread_title:  error in equation? 

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

message: 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)
thread_title:  false what? 

message: 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
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Yes, the fact that something can be improved on doesn't mean that it isn't already "good".
Regula Falsi, even without improvement, always converges, and usually considerably faster than Bisection. 
Yes there are situations that can slow Regula Falsi down, even to a prohibitive degree. But often those situations are ones that would prevent Newton's method or Secant from converging at all.
Some improvements on ordinary Regula Falsi include the Illinois version, Pegasus, and the Anderson-Bjőrk version. 
Those methods usually avoid the slowdowns that can happen to Regula Falsi. In general they do a good job of avoiding the problems that difficult equations can cause--something that is a problem for all root-finding, equation-solving methods.
Illinois is pretty good for such a simple improvement. In Galdino's "A family of Regula Falsi Methods", he reports numerical tests that he did. In his tests, Anderson-Bjőrk was the clear winner, for simple roots.
For multiple roots, no method improved significantly on Bisection, and the only ones that even did as well as Bisection were three new ones proposed by Galdino. But, even they didn't improve a lot on Bisection. ...And, as I said above, Anderson-Bjőrk was the clear winner with simple roots--a kind of problem in which the best methods were a lot faster than Bisection.
--MichaelOssipoff (talk) 17:27, 10 December 2015 (UTC)
thread_title:  Bad method? 

message: 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)
thread_title:  Indian mathematics 

message: http://books.google.com/books?id=AG2XBCmxYcUC&pg=PA157#v=onepage&q&f=false
http://muslimheritage.com/topics/default.cfm?ArticleID=993
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)
thread_title:  Double False position method originated in China, spread to Europe via the middle east and then returned to China via the Jesuits 

message: Around December 8th or 9th, I added text to the article, pointing out that "False Position" is a ridiculous mis-translation of Regula Falsi.
I told why: 
In Latin, adjectives must agree with their noun in gender, number and case.
("case" refers to how the noun is used-subject, object, etc.)
"Regula" is feminine, nominative singular. "Falsi" is either masculine nominative plural, or masculine or neuter genitive singular.
Even if you say that maybe "Regula" is masculine with feminine form, that still leaves the blatant disagreement in case, number, or both.
"Falsi", as an adjective, doesn't agree with "Regula" as a noun. 
Obviously "Falsi" is a noun.
"Regula" means "Rule" (in the sense of a regulation), or "Ruler" (straight-edge). But "Regula" was also used to refer to straight things other than a ruler.
"Falsus", or "Falsum", as a noun, means "Falsehood".
The best suggestion for the meaning of Regula Falsi is:
Straight Line of Falsehood
(because "Regula" can refer to straight things other than a ruler).
That's because Regula Falsi indeed uses a false assumption that the function is linear.
As I said, I added that text to the article.
Someone removed it within about 2 days. Why? Because you found an "authoritative source" that you could cite for the "False Position" translation? I don't care how authoritative your source was. Regula Falsi couldn't be Latin for False Position. 
Making the embarrassment worse still, you have "False Position Method" as the article's title.
The person who deleted my comments about the ridiculous "False Position" translation said that the accuracy of the name isn't relevant to the fact that it's used. ...but it's relevant to the matter of whether it makes any sense or should be used.
And, if we're going to make up a name that differs in meaning from the classical name, then at least make up something that has some descriptive value. Every iterative approximation uses and gives "false-positions". The name "Regula Falsi" specifies something that is straight-linear and a falsehood.  That's a good description of the straight line used in Regula Falsi.  — Preceding unsigned comment added by 108.132.202.166 (talk) 21:54, 10 December 2015 (UTC)
replies: text: An article like is probably not watched by many active editors so it may take quite a long time before someone who understands the topic and the terminology sees the changes or discussions (I am not that person). The edit on 8 December 2015 which I reverted was diff. Regardless of its accuracy, that text is not appropriate because the article makes no claim about the terms "false position method" and "regula falsi" other than they are both used to refer to the technique discussed. I agree that an encyclopedic article would benefit from a brief discussion of the origin of the name, but it would need a reliable source. I asked for assistance at WT:WikiProject Mathematics#False position method. Johnuniq (talk) 23:37, 10 December 2015 (UTC)
replies: text: While the Latin scholar may be correct about this point, the revert was necessary as this is WP:SYN and not relevant to this article for the simple reason that the term false position was translated into Latin and not from it. 
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You haven't shown that. 
"Regula Falsi" is not a valid Latin translation of "False Position". So, how do you support a claim that Regula Falsi is an attempted Latin translation of False Position?
Suppose, hypothetically, that an Italian expression meaning "False Position" were in use in 1591, and that, a century later, it was replaced by Regula Falsi, a Latin term.
Does that make Regula Falsi a Latin translation of (the Italian for) False Position?
Of course not. All that can be said is that Regula Falsi replaced False Position (or, rather, the Italian expression with that meaning). There's no reason to believe that Regula Falsi was intended as a translation for False Position. In fact, the fact that Regula Falsi is not a valid Latin translation of False Position, weighs against such a claim.
--108.132.202.166 (talk) 13:22, 11 December 2015 (UTC)
thread_title:  Accuracy of the name "regula falsi" 

message: My initial post about this was removed, presumably because I posted it at the wrong place (at the top of the page, above the official page-heading).
So then, let me post it here, in the usual way of adding a section to the "talk page":
Around December 8th or 9th, I added text to the article, pointing out that "False Position" is a ridiculous mis-translation of Regula Falsi.
I told why: 
In Latin, adjectives must agree with their noun in gender, number and case.
("case" refers to how the noun is used--subject, object, etc.)
"Regula" is feminine, nominative singular. "Falsi" is either masculine nominative plural, or masculine or neuter genitive singular.
Even if you say that maybe "Regula" is masculine with feminine form, that still leaves the blatant disagreement in case, number, or both.
"Falsi", as an adjective, doesn't agree with "Regula" as a noun. 
Obviously "Falsi" is a noun.
"Regula" means "Rule" (in the sense of a regulation), or "Ruler" (straight-edge). But "Regula" was also used to refer to straight things other than a ruler.
"Falsus", or "Falsum", as a noun, means "Falsehood".
The best suggestion for the meaning of Regula Falsi is:
Straight Line of Falsehood
(because "Regula" can refer to straight things other than a ruler).
That's because Regula Falsi indeed uses a false assumption that the function is linear.
As I said, I added that text to the article.
Someone removed it within about 2 days. Why? Because you found an "authoritative source" that made the same error? That obedient copying policy is what propagates an error forever (if allowed to).
Can you cite a Latinist who says that Regula Falsi means False Position? Read a page or two about Latin grammar. Or ask any highschool (secondary school) freshman 1st-year Latin student. Falsi as an adjective doesn't agree with Regula as a noun. Falsi couldn't be an adjective, as I pointed out above. "False Position" is, as I said, a ridiculous mis-translation of Regula Falsi.
--MichaelOssipoff (talk) 00:00, 11 December 2015 (UTC)
replies: text: See above section. Bill Cherowitzo  (talk) 00:20, 11 December 2015 (UTC)
replies: text: To add to the above discussion: it doesn't matter whether it's a bad translation; what matters is that "false position" is the standard English-language name for this method. See WP:COMMONNAME. —David Eppstein (talk) 00:22, 11 December 2015 (UTC)

text: So lobby the textbook authors to change their terminology. But we have to follow them here, not lead them. See WP:SOAPBOX. —David Eppstein (talk) 00:48, 11 December 2015 (UTC)

text: I'm not versed in Latin; you could well be right about a bad translation. But for the purposes of Wikipedia, the quality of the translation may be irrelevant. Wikipedia articles are descriptive of a topic, not prescriptive. They summarize the topic as it is described in reliable sources. False position and regula falsi are often treated as names for the same algorithm or class of algorithms. 
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Yes, I don't deny that, and I concede that Wikipedia's policy is not to promote new usages. But, as you said, both names are widely-used and well-established. That means that Wikipedia isn't compelled to use one instead of the other. 
So, which one should be chosen?: The one that's more descriptive ("Straight Line of Falsehood"), with widespread usage back to 1690, or the one that is less descriptive and evidently a miss-guessed translation of the other?
You're free to choose. Or, I should say, we are free to choose. So (and it wouldn't violate Wikipedia policy at all) let's use, in the title and within the article, the name that is better, with regard to descriptiveness and legitimate origin.
Choose "False Position" if you think that it's better in some way (but say why it's better), not because Wikipedia policy requires it--it doesn't.
--108.132.202.166 (talk) 11:49, 11 December 2015 (UTC)
thread_title:  "False-Position" is a ridiculous mis-translation of Regula Falsi 

message: I've just added that new section, at the beginning of the article. I didn't delete any previous work. I just added my introduction to the beginning. My addition introduces equation-solving; the generalities of methods for numerical equation-solving, and the need for them; the 2-point bracketing methods in general; Bisection; and Regula Falsi (False Position).
I put my added sections first in the article because I felt that the simpler, more basic, more familiarly worded, everyday-language introduction and explanations should come first in the article, in keeping with wikipedia guidelines to that effect.
I claim that my introduction & explanation of those topics better abides by the wikipedia guidelines specifying that articles start out simple, with things that the reader will already know about, speaking in language that the reader will understand. In these article sections that I added, the purpose was to say these things in a way that the most readers will understand. That's in the spirit of wikipedia's guidelines on such matters, and that was my purpose, in adding those sections at the beginning of the article.
I understand that the status-quo has a lot of weight at wikipedia. But I ask that, before you delete my added sections, you take a look at the simple, basic, familiarly-worded, clear, direct, concise, and sound introductions and explanations that I offer.
I didn't want to delete anyone else's work. Because the previous, already-existing article emphasized historical meanings for False Position, and its earlier forms, and my sections don't, I added the section-heading "Discussion from Historical Context" at the beginning of the already-existing article.
If anyone is inclined to delete my additions, then can we discuss it here first? I posted this announcement and discussion of my edits, and all I ask is that we have some discussion here before anyone starts deleting my added sections.
--MichaelOssipoff (talk) 01:16, 22 December 2015 (UTC)
thread_title:  I've added a new, simpler, more basic intro to eq. solving, bracketing-methods, Bisection, & Regula Falsi. 

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thread_title:  External links modified 

message: The term "method of false position" has consistently been more common than "false position method" or "rule of false position" during the 20-21st centuries, according to Google ngrams.
This article should be moved to Method of false position.
Comments? --Macrakis (talk) 03:26, 19 July 2019 (UTC)
replies: text: Personally I would prefer to move it to regula falsi. --Trovatore (talk) 04:10, 19 July 2019 (UTC)
replies: text: Silly me, I didn't plot that on ngrams. And sure enough, regula falsi turns out to be more common than the alternatives! I will start by putting that in first position in the lead. --Macrakis (talk) 05:47, 19 July 2019 (UTC)

text: do search results on “false position method” include false-position, with hyphen? Incnis Mrsi (talk) 16:37, 19 July 2019 (UTC)
replies: text:   Yes, they do, but if you look at the "false+position+method" search results (I suggest setting page size to 100), you'll find that the variant with the hyphen is rare, even if it is arguably more correct grammatically. --Macrakis (talk) 17:05, 19 July 2019 (UTC)
thread_title: Name of article

message: In the article it is claimed (section "History") that "Regula Falsi appears as the Latinized version of Rule of False as early as 1690".
There is at least one book of Gemma Frisius, in which the terms appears already in 1545: 
#https://gallica.bnf.fr/ark:/12148/bpt6k58333155/f63.double.r=.shift#
So the whole section on how the term evolved should probably be reworked.  — Preceding unsigned comment added by P-flowgie (talk • contribs) 13:56, 27 October 2020 (UTC)
thread_title:  History of the notion "Regula falsi" 

message: Added a famous root finding problem from The Nine Chapters.
* Liu Hui et al. The Nine Chapters on the Mathematical Art Copyright (C) 263 Academy of Wei & Jin Dynasties
* Shen Kangshen, The Nine Chapters on the Mathematical Art, Oxford University Press 1999. Copyrighted in the United States until 2091
--205.175.118.10 (talk) 04:29, 1 December 2021 (UTC)
thread_title:  Root finding example