Talk:Fibonacci

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Copyvio[edit]

This article is copyrighted, you can check the original article and the license here: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html 82.54.140.235 01:06, 12 December 2005 (UTC)

Removed copyvio material, reverted to this version: http://en.wikipedia.org/w/index.php?title=Leonardo_of_Pisa&diff=prev&oldid=30500067 which appears to have been the last version before the introduction of the copyvio material. --Francis Schonken 17:17, 25 December 2005 (UTC)

Requested move[edit]

The reasons for move copied from the entry on the WP:RM page:

Voting[edit]

Add *Support or *Oppose followed by an optional one-sentence explanation, then sign your vote with ~~~~
  • Support --Francis Schonken 17:30, 25 December 2005 (UTC)
  • Support, but perhaps we should add a disambig message for the numbers at the top of the page because I think they are what many people will be looking for. Stefán Ingi 15:57, 26 December 2005 (UTC)
  • Support with disambig message at top. Leonardo Pisano would be my second preference. Rd232 talk 11:49, 27 December 2005 (UTC)

Discussion[edit]

Okay, I did a bit of searching around. This is how other online encyclopedias list the guy:

  • Britannica — Leonardo Pisano (English: Leonardo of Pisa, original name: Leonardo Fibonacci)
  • Columbia — Leonardo Fibonacci (a.k.a. Leonardo da Pisa)
  • Encarta — Leonardo Fibonacci (a.k.a. Leonardo of Pisa)

This gives us four possibilities for our article title. Searching for them all on boos.google.com yields this:

  • 69 pages on "Leonardo da Pisa"
  • 427 pages on "Leonardo Fibonacci"
  • 744 pages on "Leonardo of Pisa"
  • 1350 pages on "Leonardo Pisano"

I'm keeping in mind this sentence from WP:UE:

If you are talking about a person, country, town, movie or book, use the most commonly used English version of the name for the article, as you would find it in other encyclopedias and reference works. This makes it easy to find, and easy to compare information with other sources. For example, Christopher Columbus, Venice.

It's a tough call. I'll have to think some more about it. - Haukur 12:08, 26 December 2005 (UTC)

I didn't suggest to change the page name to "Leonardo Fibonacci", but to "Fibonacci", which yields 17300 hits at books.google.com. Even the odd computer programmer that names a computer routine "Fibonacci" still refers to the mathematician.
In several of these books one can find descriptions in the sense of:

...Leonardo of Pisa , who is better known by his nickname Fibonacci,... (quote from Fibonacci Numbers - emphasis added)

Re. Britannica reference: I think wikipedia's appreciation of Britannica has radically changed lately, see http://www.nature.com/news/2005/051212/full/438900a.html - How's Wikipedia ever going to get rid of Britannica's errors if we keep referring to them?
And "original name: Leonardo Fibonacci" (as you quoted it from Britannica) is an error: Fibonacci is a nickname, not some sort of "original last name". Leonardo of Pisa is best known by his nickname, which is "Fibonacci", and that name is unambiguous (he didn't even have "less notorious relatives" that had the same name). Note that also "of Pisa/Pisano/da Pisa" is not a last name, it's just a "of <location>" format in several languages, but the use of the nickname largely supersedes all use of "<first name> of <location>" formats (I mean, of the three languages taken together). "Leonardo Fibonacci" is (1°) an error; and (2°) fairly seldomly used.
For completeness, one of his books (the Flos) he began with "Incipit flos Leonardi bigolli pisani ..." which means something like "Here starts Flos (= The Flower) by Leonardo bigolli of Pisa" - where historians think also "bigolli" rather refers to a nickname than anything that could be called a last name ("bigolli" is supposed to be an Italian word with a Latin inflection). But that nickname fell in oblivition, while "Fibonacci" stayed.
--Francis Schonken 14:50, 26 December 2005 (UTC)
Hmm... Maybe so. But I'm not entirely convinced that the Fibonacci page shouldn't be a disambiguation page rather than redirecting here. Someone typing Fibonacci into the search box may well be looking for something on Fibonacci numbers (or some other mathematical concept) rather than the mathematician himself. And it seems a bit strange to omit the only name everyone agrees on — Leonardo — from the article title. - Haukur 14:58, 26 December 2005 (UTC)
Everyone agrees on Sting's first name ("Gordon") and on his last name ("Sumner"), the combination of the two, which I think is unambiguous with any other person, has 281 hits on books.google.com (in fixed word order), yet his article is at Sting (musician). His artist's name is far less unambiguous, nonetheless Wikipedia disambiguates with a bracketed disambiguator, and not with something like Gordon Sting, which would be the same anomaly as "Leonardo Fibonacci".
The fact remains that "Leonardo Fibonacci" is how his name is listed in two out of the three English encyclopedias I'm able to check - it thus has more status than "Gordon Sting". - Haukur 16:07, 26 December 2005 (UTC)
For Fibonacci approximately only in one out of 10 cases his first name is mentioned, in the books.google.com search engine. So, what I propose in the WP:RM vote is to use the same format which is usually done with nicknames, stage names, and the like, only a disambiguator between brackets would not be needed, while there's natural disambiguation with Fibonacci numbers and the like. Note that Fibonacci currently redirects to the page of the mathematician, so I don't think anybody is thinking this should go over a disambiguation page. If you'd like to construct Fibonacci (disambiguation), go ahead, but I don't think anybody would say "a fibonacci" when they meant a "fibonacci number". --Francis Schonken 15:36, 26 December 2005 (UTC)
This is exactly what I was talking about - making the redirect into a disambiguation page. I think that might be more helpful to our readers. A quick check on Google reveals lots of references like these:
  • "Navigating through this Fibonacci and Phi site"
  • "Citations for this Fibonacci Web site"
What would you guess a "Fibonacci Web site" is? Is it a site about the mathematician? As it happens it is not in the case I came upon (though of course it could have been).
I think a person typing Fibonacci into the search box is not overwhelmingly likely to be looking for a biography of the mathematician.
We could, of course, have a disambiguation page at Fibonacci and rename this page Fibonacci (mathematician) but that is unnecessarily ugly compared to Leonardo Fibonacci or Leonardo Pisano which Encarta and Britannica use, respectively. - Haukur 16:07, 26 December 2005 (UTC)
Well, do as you like. But may I remind you that I did the same with Augustus/Augustus (honorific) some time ago: I created Augustus (disambiguation) when someone had split the emperor article (then renamed Caesar Augustus) from the "honorific" article. In the mean time the disambiguation page is completely bypassed, and nowhere mentioned (see http://en.wikipedia.org/wiki/Special:Whatlinkshere/Augustus_%28disambiguation%29 - the only link is from the list of disambiguation pages).
Note that, for example, http://www.augustus.org/ exists. Non-notable websites (see: Wikipedia:Notability (websites)) are not something to take account of when designing disambiguation. Your vague stories about something that looks like a student's website to me, is not likely to become something with a separate page in the near future. Even if it did, it would be solved by
For other uses, see Fibonacci (disambiguation).
or something similar on top of the mathematician's page. But of course, you can drive this as far as you want. I'm sure others will clean up behind you, even if I wouldn't. --Francis Schonken 17:03, 26 December 2005 (UTC)
You read such weird things into my comments. I was never suggesting that we make an article about a particular website. I was merely showing that often when people say things like "Fibonacci site" they don't mean "a site about Leonardo Pisano" but "a site about Fibonacci numbers". Thus the word "Fibonacci" alone does not necessarily indicate that the mathematician is being discussed. And someone entering 'fibonacci' into the search box is not overwhelmingly likely to be looking for this article.
On the other hand I somewhat dislike primary disambiguation and this article does contain a link to Fibonacci numbers in the first paragraph so no-one will get lost for long.
You don't have to egg me on to do something you think is stupid. I'm just trying to discuss the various possibilites, I haven't done anything yet - not even voted in your poll. - Haukur 17:16, 26 December 2005 (UTC)
I was just replying to your weird plan to make fibonacci a disambiguation page. It isn't until now, while Fibonacci redirects to the mathematician. You can make Fibonacci a disambiguation page: the only thing I wanted to remark upon is that I don't think that solution would last, even if I don't interfere. I'd rather follow Stefan's suggestion, that is: top of the page disambiguation, only with fibonacci numbers. --Francis Schonken 17:47, 26 December 2005 (UTC)
It's not a "weird plan" - it's just an idea I was throwing out for discussion. I'm still mulling it over myself and I'm interested in your opinions. What do you think the typical user typing Fibonacci into the search box is looking for? Do you, for example, think that 90% would be looking for the mathematician? 50%? Any idea? I have little. - Haukur 21:16, 26 December 2005 (UTC)
And I'm not sold on the idea that each time a programmer writes fibonacci(n) { ... } she is referring to the mathematician. Does a physicist refer to Isaac Newton every time she uses newton as a unit of force? Even an Icelandic physicist who spells it 'njúton'? Maybe in some sense, I don't know, but I'm not sure it has any bearing on the article title here.
On the other hand I am sympathetic to including Fibonacci in the article title because it is more familiar to me personally than Pisano is. But I'm trying to make a decision based on other criteria than my personal prejudices. - Haukur 15:09, 26 December 2005 (UTC)
I've been trying to find a good example to compare with but haven't been successful. I thought the Fourier disambiguation page might be it but it is complicated by the fact that there are two notable people named Fourier. - Haukur 15:11, 26 December 2005 (UTC)
Maybe try Augustus and Augustus (honorific) --Francis Schonken 15:41, 26 December 2005 (UTC)
Isn't Fibonnacci "Fi-Bonacci", or son of Bonacci? —The preceding unsigned comment was added by 74.79.228.207 (talk) 03:23, 22 March 2007 (UTC).

In any case, the name of his father is not Guglielmo Fibonacci. Some people say Guglielmo da Pisa, or G. Bonaccio (where Bonaccio was a nickname) Leonardo got the name Fibonacci only after his death, and it is assumed to be an abbreviaton of Filius Bonacci or Figlio di Bonaccio. Malo Hautus —Preceding unsigned comment added by Malo Hautus (talkcontribs) 15:02, 29 April 2011 (UTC)

Result[edit]

Moved. WhiteNight T | @ | C 02:10, 30 December 2005 (UTC)


Here is the citation requested on the front page:

Some consider him the "the most talented mathematician of the Middle Ages." Template:An Introduction to the History of Mathematics, 6th, Howard Eves, pp261

I didn't do the edit because I felt I didn't know enough about citation.

I came here looking for something on the Fibonacci sequence. I'm using the Eve's text and that quote is right out of it on page 261.

Begs 13:58, 10 June 2006 (UTC)

Please note that the quote I supplied is very similar but just a little different. Eves says, "the most talented" I suggest changing the quote in the article to match what I supplied above.24.12.168.88 05:34, 11 June 2006 (UTC)

I realized that I could handle that. I did it. 24.12.168.88 05:36, 11 June 2006 (UTC)

red herring[edit]

Sigh. Yesterday I reworded the first sentence to remove any claim that Leonardo "discovered" the notorious number sequence. So what did Bharatveer do? Put it back so that he could denounce it! This is an unnecessary stirring-up of controversy where it does not belong. Yes it is relevant at Fibonacci number. It is not relevant in Leonardo's biography. —Tamfang 02:11, 14 September 2006 (UTC)

where is the controversy in this one? The fact that it is misattributed to Fibonacci due to Eurocentrism needs to be mentioned here.-Bharatveer 08:38, 17 September 2006 (UTC)
Why? It needs to be mentioned at Fibonacci number. It's not relevant here: this article is about Leonardo Fibonacci the man, not about mathematics (let alone about cultural imperialism). You'd have us think Leonardo spent his evenings cackling, "I'll steal someone else's work, make myself famous, and get away with it because the true inventor wasn't a Christian or even a Jew." —Tamfang 05:58, 19 September 2006 (UTC)
I hope you're not neglecting the other 194 articles that link (erroneously?) to Fibonacci number. —Tamfang 06:15, 21 September 2006 (UTC)
I believe you made a mathematical error. Its 237.Bakaman Bakatalk 00:47, 27 September 2006 (UTC)
I see 327 in all, but do not count the following as "articles": 29 redirect pages; 5 images; 20 Talk pages; 1 Category talk page; 18 User pages; 25 User talk pages; 22 "Wikipedia:" pages; 8 Wikipedia talk pages. I also exclude pages that cite Binet's formula or Binet's Equation (which redirect), since they do not show the "error". This time I'll count Category:Fibonacci numbers and two subpages of Portal:Latin America/Did you know, bringing the total to 197. —Tamfang 03:09, 28 September 2006 (UTC)

erroneously[edit]

It says "He is best known, erroneously" for the Fibonacci numbers. That calls for explanation. Is it claimed that he never knew of that number sequence, or that he learned it from someone else, or what? Michael Hardy 01:50, 18 September 2006 (UTC)

His involvement with the sequence named after him is limited to an exercise on a rabbit population, where the solution involves the calculation of the first few numbers of the sequence. He did not single out the sequence as being interesting in itself. Anyway, he made far more signifificant contributions, e.g. promoting the Hindu-Arabic numerals in the Christian world at a time where we still used roman numerals. He'd be surprised to know that his fame today (at least with the majority of high school students around the world) is tied to sunflowers and such... How best to make the article reflect these facts, I'll leave to others. I gave up editing articles on Fibonacci numbers, the golden ratio and related subjects a while ago; it's too frustrating with all the nonsense so many people believe in and want to include.--Niels Ø 07:07, 18 September 2006 (UTC)
Rather than getting frustrated ,Pls see this reference Fibonacci_Encyl.Brit . " Except for his role in spreading the use of the Hindu-Arabic numerals, Leonardo's contribution to mathematics has been largely overlooked. His name is known to modern mathematicians mainly because of the Fibonacci sequence (see below) derived from a problem in the Liber abaci . -Bharatveer 08:12, 18 September 2006 (UTC)
That quote is of course absolutely true. My frustration is more general - so much nonsense is being said about the golden ratio and related matters, and so little is documented by primary sources. --Niels Ø 08:49, 18 September 2006 (UTC)

Suggested External Link[edit]

Please consider inclusion of the following page on my website:

as a recreational exercise for students that illustrates Simson's discovery. Paul Niquette 20:38, 5 December 2006 (UTC)

Please excuse me (a new wikipedian) for putting this in the wrong place. I shall appreciate guidance in putting it in the right place. Paul Niquette 20:56, 7 December 2006 (UTC)


his father's nickname[edit]

At some point someone changed Leonardo's father's nickname from Bonaccio to Bonacci throughout. On grammatical grounds I think this very unlikely to be correct. Can someone defend it? —Tamfang 05:29, 30 April 2007 (UTC)

According to the math historian Tobias Dantzig, whose work I just referenced in the article, his father's nickname was Bonaccio. Br77rino (talk) 02:33, 17 October 2013 (UTC)

Information on Origin of "Fibonacci Numbers "[edit]

Fibonacci certainly did not discover the sequence named after him. The earliest known mention of the these numbers is in the ancient indian sulbhasutras written around 800 BC -500 BC . Pingala an indian mathematician (~450 BC or 200 BC) later mentions these numbers.

The Indian mathematician Virahanka (6th century AD) showed how the Fibonacci sequence arose in the analysis of metres with long and short syllables. Subsequently, the Jain philosopher Hemachandra (c.1150) composed a well known text on these. A commentary on Virahanka by Gopāla in the 12th century also revisits the problem in some detail.

So it is certain that the numbers should be more appropriately named "SulbhaSutra Numbers " instead of Fibonacci Numbers . Of course eurocentric math historians always make every effort to deny the indians due credit and show them as mere imitators of european mathematicians . —Rajarshi

We've been over this till we're sick of it. It does not belong in this article. Go to Fibonacci number and raise the issue there if that article doesn't assign credit properly. —Tamfang 08:33, 13 August 2007 (UTC)and also (BUTT)

Part of a sentence seems not to make sense[edit]

Nevertheless, the use of decimal numerals did not become widespread until the invention of printing almost three centuries later, in 1585 (see, e.g., Ptolemy's world map printed in 1482 by Lienhart Holle in Ulm).

I don’t know what is being got at. We say that the Liber abaci was ‘published’ (whatever that means, exactly) in 1203 and that Fibonacci died in 1250: so 1585 is more than 300 years later. Somehow the Ptolemaic map of 1482 (printed before printing had been invented) is relevant to the acceptance (or non-acceptance?) of the Hindu-Arabic numeral system in Europe: but we don’t say how. Somehow the invention of printing is relevant to the spread of the system: again we need to say how. Is it simply that the book—or other texts based on it—only became sufficiently widespread once moveable-type printing had become widespread? Or that Arabic numerals are somehow easier to print than Roman ones? Or what?

I am sure that the sentence must have meant something at one time, but it seems to have been wikified into nonsense, so I’ll cut it off in its prime for now. —Ian Spackman (talk) 23:00, 29 November 2007 (UTC)

in finance[edit]

The Fibonacci Sequence (Fibonacci Retracement, Fibonacci Fan, Fibonacci Time Zone, and Fibonacci Arc) were often used by global traders (Forex, Stock, Commodities) as the most powerful indicator for predicting movement of the market prices.

I'm not happy about the language, given that the power of the indicator is controversial. A reference to how FNs are useful here would also be good. —Tamfang (talk) 10:59, 17 February 2008 (UTC)

Nationality[edit]

I find it strange to call Fibonacci italian and print the italian flag in the article. As far as I know both the country and the flag didn't exist when he lived. Have I missed a Wiki-policy or what? Jon Tofte-Hansen (talk) 13:45, 19 May 2008 (UTC)

I strongly second this remark, Pisa was one of the most powerful states at that time and Italy as we know it today was only to be formed an odd 700 years later in the 19th century. This is indeed not up to the standards of Wikipedia. Another concept not really known at those times was "nationality" it really seems to make sense to remove the Italian flag, as much as I like Italy BTW, I used to live there for some years :). Of course it would be nice to say something like Pisa located in nowadays Italy or something of that sort.

Cheers and keep the good work up, of course nobody is everything writing comments in the discussion pages of the thousands of articles we are consulting and that are perfectly correct!

Robert —Preceding unsigned comment added by 88.139.30.219 (talk) 10:44, 25 May 2008 (UTC)

,,,,,,,,,,,,,,,,,,,,,,,,,,,,, —Preceding unsigned comment added by 91.107.17.98 (talk) 15:16, 13 October 2008 (UTC)

The comments above are absurd. The state of Italy did not exist until the 19th century. The word Italia as the name of the penninsula dates back to long before Fibonacci's time. And that's where Fibonacci lived. It's like saying he didn't live in Europe because no state called "Europe" existed. Or like saying Plato was not a Greek because no state called Greece then existed. Michael Hardy (talk) 22:09, 3 August 2009 (UTC)

Of course he lived in Italia! Nobody questions that. The discussion is about the flag (which somebody has removed now :) ) and the term "nationality". He lived in the geographic/linguistic/cultural area Italy allright, and in that sense you can call him Italian. But because no governmental entity of that name existed at that time the term Italian can be misunderstood as refering to a state rather than a geographic/linguistic/cultural relationship - especially in connection with the word nationality, which in modern sense meanse more than just "place of birth". Jon Tofte-Hansen (talk) 12:35, 14 August 2009 (UTC)

It is strange altogether on WP this obsession with nationalism, also religion and ethnicity, retrospectively applied and quite out of context. Many subjects of biographies would be amazed at how they are described here. As I understand it our subject was born in The Almohad Empire, probably recognised as a foreigner and citizen of the Republic of Pisa. Hakluyt bean (talk) 12:14, 17 April 2012 (UTC)

Zero is not a Fibonacci number.[edit]

Does anyone have any insight as to why 0 precedes the list of Fibonacci numbers here?


130.56.71.132 (talk) 01:37, 2 April 2009 (UTC)


Because it's the zeroth Fibonacci number, of course. —Preceding unsigned comment added by 24.13.90.226 (talk) 07:44, 13 January 2010 (UTC)

Removed from the list along with the second "1". It is a Fibonacci number in modern mathematics but was not one of the numbers that Fibonacci included in his list, which began "1, 2, 3, 5, 8...233". Since this article is about Fibonacci the mathematician, not the modern history of Fibonacci numbers, the list in this article should follow his list. Also removed the discussion of Golden Ratio, just leaving a little link, since he does not discuss it either. -- Michael Scott Cuthbert (talk) 22:46, 8 June 2013 (UTC)

Laurence Sigler information?[edit]

Can someone provide me with an official birth and death dates for Laurence Sigler? I have hard time finding ANY information about him online, even though he did a great amount of work to help translate Fibonacci. --Drozdyuk (talk) 13:27, 17 May 2010 (UTC)

He received his Ph.D. from Columbia University in 1963[1] and took an appointment at Hunter College.[2] His translation of Liber Abaci (2002) lists him as deceased, and as affiliated with Bucknell University. I can find very little about him at the Bucknell web site, just some course listings. According to this review of his translation (in French), he died in 1997. —David Eppstein (talk) 00:00, 3 May 2011 (UTC)

Fibonacci Bamboozlement[edit]

Should the article cover any of this? http://www.cut-the-knot.org/Generalization/CevaPlus.shtml#bam

The so called "dissection bamboozlement", 64=65 illusion/paradox. Mil 20:33, 18 May 2010 (UTC)

No, this is primarily an article about a medieval mathematician, not about other mathematical ideas named for him. (it is interesting though). -- Michael Scott Cuthbert (talk) 02:42, 17 October 2013 (UTC)

Fibonacci Sequence & The Rabbit Problem[edit]

First, it seems as though the "Fibonacci Sequence" page should be a sub-category on the "Fibonacci" page.

It is interesting that the Fibonacci numbers were seen earlier than the time of Fibonacci in Indian mathematics, but because of one person, Edouard Lucas (a French number theorist), Fibonacci is seemingly given all of the credit. Lucas named the sequence after he saw it in the rabbit problem in Fibonacci's book Liber Abaci. It's an interesting problem because it assumes that all of the rabbits mature at exactly the same rate, they are all reproductively successful, and none of them die.

"A man put one pair of rabbits in a certain place entirely surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year, if the nature of these rabbits is such that every month each pair bears a new pair which from the second month on becomes productive?"

[Burton, David M. The History of Mathematics: An Introduction. 7th ed. New York: McGraw-Hill, 2011. 287.]

The number of young pairs of rabbits each month is the Fibonacci sequence (1,1,2,3,5,8,13,21...). It almost seems as though Fibonacci lucked out with this problem and its specific restraints (a bold statement, I know). Would Indian mathematics have received credit for the sequence had Fibonacci not proposed this problem? Or would he possibly have discovered it some other way? 199.245.238.2 (talk) 23:47, 2 May 2011 (UTC)Kelsey, History of Mathematics student at Saint Martin's University

With Fibonacci's use of the rabbits, I would assume he knew it was illusory to put such restraints on the rabbit population under question. It seems as if he used the rabbits since they were indeed a very prolific animal that had relatively normal birth cycles and then followed them and resultantly found the familiar sequence.

Ward.E (talk) 19:57, 3 May 2011 (UTC)

Fibonacci receiving credit for the sequence is probably due to the great influence of Western teachings in our textbooks. If India had become a great power like Europe did from the 17th century onward then perhaps more Indians would be given credit in modern text books. It seems to be another case of 'victors' writing history.

As for Fibonacci 'lucking out' with this problem he probably realized some correlation between the numbers and then tweaked the problem set to fit his purpose. Whether or not he just randomly thought of the correlation or was looking for real world correlations is another matter entirely which I doubt will ever be answered. There is a certain amount of credit that should automatically be given for recognizing something like that though.

76.121.129.155 (talk) 03:19, 4 May 2011 (UTC)Alex Kinney - St. Martin's University

The "victors writing history" is a very good point, sadly. It would be interesting to see how history books would be written had this not been the case. Fibonacci definitely deserves credit for recognizing the sequence especially because it contributed work with the Golden Ratio. 199.245.238.2 (talk) 04:12, 4 May 2011 (UTC)Kelsey, History of Mathematics student at Saint Martin's University

Edit request on 6 January 2012[edit]

Please change the name Guglielmo Fibonacci to Guglielmo Bonacci, in accordance with the reference information. (http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html)

216.114.63.233 (talk) 12:49, 6 January 2012 (UTC)

Done. Thanks for your vigilance! Favonian (talk) 14:35, 7 January 2012 (UTC)

Edit request on 1 June 2012[edit]

I would like to suggest three corrections to the article on Fibonacci.

  1. In the first sentence of the second paragraph, the word "publication" is inappropriate for a work that was handwritten and copied (not printed) centuries before the invention of printing. Therefore, I suggest that the phrase "primarily through the publication in 1202 of his Liber Abaci (Book of Calculation)" be changed to "primarily through his authorship in 1202 of Liber Abaci (Book of Calculation)".
  2. In the third sentence of the section on Liber Abaci, the mention of lattice multiplication is inaccurate. Although it is widely stated on various Internet pages that Liber Abaci demonstrated lattice multiplication, this doesn't stand the test of evidence. No copy of the first edition (1202) has survived, and examining both the Boncampagni and Sigler editions of the second (1228) edition shows no evidence of lattice multiplication, even though the work does use many other algorithms of decimal place-value arithmetic. Therefore, I suggest that the phrase "The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions..." be changed to "The book showed the practical importance of the new numeral system, using decimal place-value arithmetic and Egyptian fractions...".
  3. In the Bibliography section where the work Practica Geometriae is listed, no English version of the work is cited, and the mention of trigonometry is inaccurate inasmuch as the work has virtually no trigonometry in it. Therefore, I suggest that the phrase "a compendium on geometry and trigonometry" be changed to "a compendium of techniques in surveying, the measurement and partition of areas and volumes, and other topics in practical geometry", and this should be followed by: (English translation by Barnabas Hughes, Springer, 2008).

--- Prof. Randy K. Schwartz (Wikipedia username: Rks22)

 Department of Mathematics
 Biomedical Technology Center
 Schoolcraft College
 18600 Haggerty Road
 Livonia, MI 48152-2696  USA
    email rschwart@schoolcraft.edu
    voice 734/462-4400 extn. 5290
    fax   734/462-4536

Rks22 (talk) 04:00, 1 June 2012 (UTC)

I suspect the part about Egyptian fractions is left-over Milo Gardner cruft. Would it be appropriate in #2 to just say "The book showed the practical importance of the new numeral system, using decimal place-value arithmetic"? —David Eppstein (talk) 04:42, 1 June 2012 (UTC)
1) Done
2 and 3) Not done: please provide reliable sources that support the change you want to be made.
Mdann52 (talk) 15:53, 1 June 2012 (UTC)

I concur with the suggestion by David Eppstein to just say, "The book showed the practical importance of the new numeral system, using decimal place-value arithmetic."

The reliable sources for my assertion #2, that Fibonacci's Liber Abaci did not demonstrate lattice multiplication, are from examining Liber Abaci itself:

Latin version: Boncompagni, Baldassarre, Scritti di Leonardo Pisano, vol. 1 (Rome: Tipografia delle Scienze Matematiche e Fisiche, 1857)
English translation: Sigler, Laurence E., Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation (New York: Springer Verlag, 2002).

In Chapter 3 of his Liber Abaci, Fibonacci describes a technique of multiplication by "quadrilatero in forma scacherii" (“quadrilateral in the form of a chessboard”). In this technique, the square cells are not subdivided diagonally, which means that the “carry digits” must be remembered or recorded elsewhere. This is in contrast to lattice multiplication, a distinctive feature of which is that the cells of the quadrilateral can be filled in in any order desired. Swetz compares and contrasts multiplication by gelosia (lattice), by scacherii (chessboard), and other tableau methods: Swetz, Frank J., Capitalism and Arithmetic: The New Math of the 15th Century, Including the Full Text of the Treviso Arithmetic of 1478, Translated by David Eugene Smith (La Salle, IL: Open Court, 1987), pp. 205-209.

The reliable sources for my assertion #3, that Fibonacci's Practica Geometriae had virtually no trigonometry, are from examining Practica Geometriae itself:

Hughes, Barnabas, ed., Fibonacci’s De Practica Geometrie (New York: Springer Verlag, 2008).

The characteristic feature of trigonometry is the solution of triangle problems by use of standard ratios among the sides of right triangles, today known as the sine, cosine, etc. The discussion of such ratios is confined to only a few pages of De Practica Geometrie (section 3.1 in Hughes's text), and the ratios are not named and used in solving triangle problems. Historically, trigonometry was applied to astronomy, not to surveying problems.

Rks22 (talk) —Preceding undated comment added 23:47, 3 June 2012 (UTC)

Death[edit]

Is there any evidence that he died in Pisa? The source Eight Hundred Years Young states "No one knows when Fibonacci died nor under what circumstances his death occurred." A featured feedback comment asks about his death, maybe the article could more clearly reflect the lack of information? Why the feedback in question is flagged as abuse five times is a mystery to me.. Ssscienccce (talk) 04:47, 10 January 2013 (UTC)

The evidence is that one of the two sources for that part (the Encyclopedia of Mathematics) says that he died in Pisa. —David Eppstein (talk) 04:59, 10 January 2013 (UTC)
I've seen it, but that could be an assumption, no reference is given and the sources I've read all state that the decree made by the Republic of Pisa in 1240 in which he is awarded a salary is the last known document which refers to Fibonacci.

Another point: There are 246 feedback comments, many of them are about the lack of information. The article should really mention that very little is known about his life. Without that knowledge, readers will always assume it's a Start-Class article, even when it's complete. Ssscienccce (talk) 05:50, 10 January 2013 (UTC)

The feedback comments are why there's already a line in there saying that we don't know when he died. Before that, there was nothing. But you're welcome to try making the nothing bigger. —David Eppstein (talk) 05:58, 10 January 2013 (UTC)

Limit of a Fibonacci Sequence[edit]

"Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence."

Of course he didn't. The concept of the limit wasn't developed until 400 years after his death... 2crudedudes (talk) 18:56, 11 November 2014 (UTC)

Recent revert[edit]

There are two issues that caused my recent revert to an earlier version of the page. The first concerns the replacement of Europe with Western World. This is a bad edit since Western world is ambiguous in meaning (see the article). Its older meaning was synonymous with Europe, but its modern meaning includes the Americas, Australia and New Zealand (among other places). Fibonacci introduced the Hindu-Arabic numerals to Europe and this spread to the Western world with the expansion of the influence of Europe (as did the definition of the Western world). I have seen the references to the western world that other editors have mentioned, but these do not appear in reliable sources. The more accurate statement is that he introduced the numerals to Europe, so I reverted to that. The other issue was the little piece of puffery about Fibonacci being one of the greatest mathematicians of all time. In support of this there were three websites given. The first two had no authorship attributed, nor criteria for inclusion given, and can't be considered as anything more reliable than blogs. The third was a meta-analysis of several lists produced by reliable sources and Fibonacci does not even appear on the list. I conclude that the support for this statement in the article is not present. Bill Cherowitzo (talk) 18:34, 10 February 2015 (UTC)

I agree with this, and would add that the evaluation as "one of the greatest", however well sourced, should not have been in the lead without being covered in more detail down below: Noyster (talk), 18:48, 10 February 2015 (UTC)
Your revert lost a good change in a wikilink from Italy (the modern country that was not formed until long after Fibonacci's death) to Italians (the ethnicity that Fibonacci came from) but otherwise I agree with it and your reasoning for it above. —David Eppstein (talk) 18:53, 10 February 2015 (UTC)

Agree with "Western World" revert. I had also reverted the "Europe" -> "Western World" change previously for exactly the same reason - the Western world in Fibonacci's time was Europe and not the current usage. Squinge (talk) 20:27, 10 February 2015 (UTC) (Modified comment - Squinge (talk) 12:08, 13 February 2015 (UTC))

@David thanks for having fixed the wrong wikilink. As you "Wcherowi", before reverting an edit, please read carefully. --115ash→(☏) 10:57, 12 February 2015 (UTC)

You can find several reliable sources which state that he is one of the greatest mathematicians of the history (many ranked him as one the top 5). Then everyone knows about his notability, common! You may modify that phrase. --115ash→(☏) 11:15, 13 February 2015 (UTC)

Fibonacci's notability is not in question. The issue is the peacock phrasing of one of the "greatest mathematicians". If you have reliable sources please provide them. Those given in the article, as I have said, are either not reliable or do not support the claim. Bill Cherowitzo (talk) 18:19, 13 February 2015 (UTC)
  • Folks, can I suggest you stop edit warring about this until there's a consensus here? Squinge (talk) 12:07, 13 February 2015 (UTC)

Requested move 27 April 2015[edit]

FibonacciLeonardo Fibonacci – Shouldn't be Leonardo Pisano Bigollo as per WP:RECOGNIZABLE, however the first name "Leonardo" should be OK, seen that people confuse it with ---> Fibonacci number. 115ash→(☏) 13:12, 27 April 2015 (UTC)