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:There is no disinformation in the quoted passage about Al-Biruni's calculation of the Earth's radius. You have simply missed the point of it entirely, which is that Al-Biruni was the ''first'' person known to have calculated the Earth's radius ''using the method described''. That method is completely different from the one used by Eratosthenes, and is potentially much less expensive to apply, in that it doesn't require one to carefully measure the distance between two points some 100 or more km apart (in fact, about 900km in Eratosthenes's case). As it happens, the method isn't very useful in practice because the effect of atmospheric refraction on the measurements is not accurately determinable, but that doesn't make it entirely uninteresting.<br> :There is no disinformation in the quoted passage about Al-Biruni's calculation of the Earth's radius. You have simply missed the point of it entirely, which is that Al-Biruni was the ''first'' person known to have calculated the Earth's radius ''using the method described''. That method is completely different from the one used by Eratosthenes, and is potentially much less expensive to apply, in that it doesn't require one to carefully measure the distance between two points some 100 or more km apart (in fact, about 900km in Eratosthenes's case). As it happens, the method isn't very useful in practice because the effect of atmospheric refraction on the measurements is not accurately determinable, but that doesn't make it entirely uninteresting.<br>
:]&nbsp;<small>(]&nbsp;·&nbsp;])</small> 17:19, 30 July 2013 (UTC) :]&nbsp;<small>(]&nbsp;·&nbsp;])</small> 17:19, 30 July 2013 (UTC)
::He is the second to have calculated the Earth radius. He is not a notable person for that. What's the interest to be the second. You violate the rules if edition. John Doe was the millionth to solve a second degree equation. What's the interest for that. Sincerly.] (]) 10:04, 6 August 2013 (UTC)

== Translation of French Misplaced Pages ==

=== Arithmetic ===
====Irrationnals numbers====
=====Magnitudes and irrationals=====
According to Kline,{{quote|If ] had really offered a theory of irrationals}}, there are twa possible interpretations : {{quote|the first is that magnitudes themselves could be taken to be the irrational numbers, and the second is that the ratios of two magnitudes could be the irrational numbers}}<ref>Mathematical Thought from Ancient to Modern Times, Volume 1, page 72, Oxford University Press, 1972</ref>

=====The use of irrationnals=====
Babylonians used tables of cibic and square roots, providing accurates approximations like {{sqrt|2}} = 1,414213…<ref>According to {{Harvsp|Kline|1972}}, one cannot say if Babylonians were aware of the existence of an infinity of decimals or sexagesimals for the irrationnal numbers or if they believed they can convert them in a finite number of sexagesimal if they have more place in the board they used.</ref>{{,}}<ref>{{Harvsp|Kline|1972|p=8}}.</ref>. The discovery of irrationnal numbers was made by ] (V th century)<ref>{{Harvsp|Kline|1972|p=32}}.</ref>. The proof of the irrationality of {{sqrt|2}} was made by ] using an "ab absurdo" demonstration<ref>Reductio ad absurdum.</ref>{{,}}<ref name="mk33">{{Harvsp|Kline|1972|p=33}}.</ref>. ] has proved the irrationality of {{sqrt|3}}, {{sqrt|5}} and {{sqrt|7}}. ] realised a first classification of irrationnal numbers<ref name="mk33" /> . ] analysed all the possibilities for lines that could be mathematizied by <math>\sqrt{\sqrt{a}+\sqrt{b}}</math> (a et b are lines). Romans of Alexandria<ref>qualified often by Alexandrians, greek mathématicians belonging to the Roman Empire</ref>, at the opposite of the Greek who did not recognize the irrationals like numbers, used them like numbers for measuring the lenght, the area and the volume<ref>{{Harvsp|Kline|1972|p=104}}.</ref>. Hindus (200-1200) used correct operations with irrational numbers, like addition and substraction. The principle is : <math>\sqrt{a}+\sqrt{b}=\sqrt{(a+b)+2\sqrt{ab}}</math><ref name="mk185">{{Harvsp|Kline|1972|p=185}}.</ref>. The persian mathematician ] (1048-1122) stated that all ratio of measure, rational or irrational, could be named a number<ref>{{Harvsp|Kline|1972|p=191-192}}.</ref>. The Arabs copied the operations on irrationals introduced by Hindus<ref name="mk192"/>. One must wait until the XVIIIth century to have a good survey of irrational numbers. In 1727, Bernard le Bovier de Fontenelle stated that {{quote|the irrational numbers<ref>(French) les nombres irrationnes se trouvent en une quantité sans comparaison plus grande que les nombres rationnels</ref> are proportionnaly more and more important that rationnal}}<ref>Jean Mawhin, ''Analyse, fondements, technique, évolution'', De Boeck Université, Bruxelles, 1992, {{1re}} édition, p. 38.</ref>

Inside the work of synthesis made by Arabs, was ] who used the irrationnal numbers and ]. Another arab mathematician of the IX th century, ] who translated greek manuscripts but was also studying the ].

====Positional numeration====
In the twelfth century, ] translations of ]'s ] on the ] introduced the ] ] to the ].<ref name="Struik 93">{{harvnb|Struik|1987| p= 93}}</ref> His '']'' presented the first systematic solution of ] and ]s. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources.<ref>{{harvnb|Rosen|1831|p=v&ndash;vi}}; {{harvnb|Toomer|1990}}</ref> He revised ]'s '']'' and wrote on astronomy and astrology.

In 628, the Hindu astronomer and mathematician ] published ''Brahma Siddhanta'', treaty where he exposed a decimal numeration exactly the same that we use today<ref>{{Ouvrage|prénom=Fernando|nom1=Corbalan|titre=Le Nombre d'or|sous-titre=Le langage mathématique de la beauté|traducteur=Youssef Halaoua, Maguy Ly et Laurence Moinereau|mois=9|année=2011|éditeur={{Lien|lang=es|trad=RBA|Groupe RBA|texte=RBA}}-]|collection=Le Monde est mathématique|numéro dans collection=1||passage=18}}.</ref>. The ] was copied by arab mathematician.
====The positional zero indicating a missing cipher====
The positionnal zero was used for the first time by Babylonians during the Seleucid period the take over by the Greeks during Alexandrian period. They used different symbols for the representation of the positional zero<ref>{{Harvsp|Kline|1972|p=132}}.</ref> comme : <math>\overline{{0}}</math>. The arab mathematician copied the idea.
====The zero as number====
Hindus treated the zero as a number. The hindu mathematician announced that the multiplication of a number by zero is equal to zero and that substract zero do not diminish a number. According to him, to divide a number by zero maintain this number unchanged<ref>Today, mathematicians say that to divide a number by zero is equal to multiply it by infinity.</ref>{{,}}<ref name="mk185" />. The arab mathematiocian copied the hindu model.
====Calculus of Pi====
The persian astronomer and mathematician ] calculated an approached value of ]. ] has calculated 3 decimals.

=== Algebra ===
The attribution to ] of the origin of algebra is discuussed since the ]<ref>G. Cifoletti, La question de l'algèbre. Mathématiques et rhétorique des hommes de droit dans la France du {{XVIe|s}} siècle, Annales, 1995, vol. 50, p. 1385-1416, {{lire en ligne|url=http://www.persee.fr/web/revues/home/prescript/article/ahess_0395-2649_1995_num_50_6_279438}}.</ref>. According to ]<ref>« Algèbre d'al-ğabr » et « algèbre d'arpentage » au neuvième siècle islamique et la question de l'influence babylonienne, Fr. Mawet et Ph. Talon, D'Imhotep à Copernic. Astronomie et mathématiques des origines orientales au moyen âge. Actes du Colloque international, Université Libre de Bruxelles, 3‑4 novembre 1989. (Lettres Orientales, Leuven, Peeters, 1992 , p. 88.</ref>, {{quote|Al-Khwarismi informe us that he has not create this branch of mathematics}}<ref>(French) Al-Khwarismi nous informe qu'il n'a pas inventé la discipline </ref>{{,}}<ref>The algebra and the algorithms of calculus</ref>. He quote, giving strenght to his argumentation, the passage of '"Al-Gabr w'al-muqabala" where Al-Khwarismi refers to "arithmetics used by a notary sollicitor"<ref>(French) arithmétiques utilisées constamment dans les affaires d'héritage et de legs</ref>{{,}}<ref>Translation of Sayili, 1962.</ref>. According to him {{quote|Al-Kwarismi only poduced a synthesis work of disciplines and algorithm, including the genuine superstructure}}<ref>(French) al-Khwarismi n'a fait "que" produire une oeuvre de synthèse des disciplines et techniques des calculateurs pratiques, y compris la superstructure "pure"</ref>{{,}}<ref>By superstructure, one can understand problems encoutered during professional life and the skill to solve them. Genuine refers to genuine mathematics or scientific mathematics used by Greek. (Summary of a note of {{Harvsp|Høyrup|1992|p=89}}).</ref>{{,}}<ref name=Hoyrup88/>. This synthesis work will play a role during the ]<ref>{{Harvsp|Høyrup|1992|p=108}}.</ref>{{,}}<ref>The auteur say also that this role is probable concerning ], but may be also to ].</ref>.
====Resolution of a system of equations====
] solved equations with multiples unknows reducing the system to one unknown and solved it. ] copied the method<ref name="mk192">{{Harvsp|Kline|1972|p=192}}.</ref>. According to Kline, the rab algebra is only rhetorical and was a backstep if we copare it to indian algebra and to Diophantus's algebra.<ref name="mk192" />.
====Equation of second degree====
The resolution of second degree equation was well-known since Babylonians<ref>{{Harvsp|Kline|1972|p=193}}.</ref>. ]<ref>The name of this mathematician, latinised in ''Algoritmi'', gived the word ''algorithm''.</ref> only explained the algebraic process by geometry.

The second treaty, ''Kitab fi'l-jabr wa'l-muqabala'' <ref>(French) Livre sur la restauration et la confrontation</ref> expose only operations on equations. He propose the resolution of ] by a completion of squares.

====Using of latin letters to represent the unknowns====
Diophante used the first letter of a word state that it is a quantity, i.e. <math>s</math> for side and even <math>s^{2}</math> to represent what he called the "power" of this quantity. ] used the same words and the same sympbolic<ref name="mk192" />.
=====Using of ''{{math|x}} '' to represent the unknown=====
Many arab books use the ''{{math|x}} '' to represent the unknown. Given the great destruction of books of mathematics during "autodafés"<ref>Like in the book Farhenheit 351</ref> (this of general ] but also this of the "vanity butcher" of]), one cannot say precisely wich mathematician (he could be also greek, indian or arabic) who used for the first time the ''{{math|x}} '' to represent the unknown. According to the well-known group of mathematicians ], {{quote|Diophante uses, for the first time, a litteral symbol to represent the unknown}}<ref>Nicolas Bourbaki, '']'', Masson, Paris, 1994, {{3e}} tirage, p. 69.</ref>{{,}}<ref>The authors insinuate that Diophantus has created the ''{{math|x}} '' in mathematics because they don't quote any arab mathematician in the chapter devoluted to algebra.</ref>

=== Geometry ===
The property of plane geometry were well-known since ] (Books XI and XIII from Eléments)<ref>{{Harvsp|Kline|1972|p=85-86}}.</ref>. These properties were used by Arabs to develop ]s. The deutch artist ] used mathematics in his work and was interested by ] after having visit the Alhambra in 1936<ref>{{Harvsp|Corbalan|2011|p=81}}.</ref>.
=== Trigonometry ===
The founder of trigonometry is ]<ref name="mk119">{{Harvsp|Kline|1972|p=119}}.</ref>. The division of the circonference of a circle in 360 degrees<ref>The circonference is divided in 60 parts, each part is divided in 60 parts of parts. The diametra is divided in 120 parts.</ref> is dued to ] of Alexandria<ref name="mk119"/>. Hipparchus calculated the number of units for a ] corresponding to a given number of degrees, and that's the same of our sinus function<ref>La corde est le double du côté d'un triangle rectangle inscrit dans un quadrant de cercle et ayant comme rayon l'hypothénuse. Un côté de l'angle droit d'un triangle rectangle est égal au produit de l'hypothénuse par le sinus de l'angle opposé.</ref>{{,}}<ref name="mk120">{{harvsp|Kline|1972|p=120}}.</ref>. ] (98 A.D.) déveloped the greek trigonometry in his books "Sphaerica" and "Chords in a circle" where one can find the concept of spherical triangle. His book "Sphaerica" has been translated in arab<ref name="mk120" />. The trigonometry was continued by Hindus. The astronomer and mathematician ] copied the works realised before<ref>According to {{Harvsp|Kline|1972|p=195}}, The Arabs made very little progress in astronomy.</ref> and uses the sinus function and tangente function in astronomy and wrote tables to calculate them. The ] is dued to chinese mathematician Kuo Chou-tching (1231-1316) who created the chou-chih calendar<ref>Philip J.Davis et Reuben Hersh, ''L'univers mathématique'', translated in french by L. Chambadal, Gauthier-Villars, 1985, p. 26.</ref>.] (]) 09:56, 6 August 2013 (UTC)
{{reflist}}

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Partially translated from french wikipedia fr:mathématiques arabesTranquil Pepere (talk) 11:27, 23 July 2013 (UTC)

Biased article

95% of the so called islamic mathematicians were Persian. Their work had nothing to do with Islam nor arabs or their culture.

The west has come to know Persians as arabs due to lack of knowledge, and the arab nationalists prey on that. 82.209.153.239 (talk) 19:01, 27 November 2011 (UTC)

Tranquil Pepere

Stop vandalism

I made an important contribution by translating the french wikipedia. What an horribilis discovery I made by seeing the history of the differents versions of wikipedia. It's a pure vandalism. Morris Kline has said about the mathematics made by Arabs and Hindus : It's not brillant. Open the book and you will see what exactly Kline think about it. Nicolas Bourbaki don't even talk about the Arabs in the chapter devoted to algebra. I am not a native. I am sure I have made errors or maybe blunders during the translation. But vandalism is not acceptable.Tranquil Pepere (talk) 13:39, 23 July 2013 (UTC)

I have reverted the recent additions by Tranquil Pepere. Reverting questionable content is not vandalism. Issues with the content include grammatical problems that make some sections incomprehensible, spelling errors, and a question of neutral POV. Tranquil Pepere, I suggest you post your proposed changes here on the talk page first, and give other editors a chance to discuss them. I've left a note on your talk page about editing in general. Dialectric (talk) 14:06, 23 July 2013 (UTC)
It is not a questionable content. It is a translation from the french wikipedia. Grammatical problems can be modified directly on the main page. If a passage is incomprehensible, in this case, you can transfert it to the talking page in order to ameliorate it. The question of neutral point of view must be discussed quoting the phrases tou estimate to be not neutral. What I see, it's vandalism. Or may be worst, a disregarding manner to welcome a non native englishman.Sincerly yours.Tranquil Pepere (talk) 14:33, 23 July 2013 (UTC)
Your changes are unacceptable. It is not the duty of other editors to wade through large masses of poorly written material to correct it; it is up to you to make it of sufficiently acceptable quality that they will be willing to let it stand. Even apart from the grammar, there are other problems with the material you have added, so please stop edit warring to keep it and describe the changes you wish to make, one by one, on this talk page.
David Wilson (talk · cont) 15:12, 23 July 2013 (UTC)
I repeat I ask to stop vandalism or worst censorhip (my contributions are made using quotations from academics professors not John Doe)Tranquil Pepere (talk) 09:45, 30 July 2013 (UTC)

Change of name : Arabic mathematics

One speak of Arabic mathematics, but it was Arabic in language primarily. Most of the scholars were Greeks, Christians, Persians and Jews.

  1. Mathematical Thought from Ancient to Modern Times, Volume 1, p.191, Morris Kline, Oxford University Press, 1972

Most of the scholars speak about "Arabic mathematic". So a change is needed.Tranquil Pepere (talk) 09:53, 30 July 2013 (UTC)

You are mistaken. "Arabic mathematic" is not even correct English. It's a solecism which would not be used by any reputable scholar with a good command of the language. The term "Arabic mathematics" is commonly used, but the final "s" cannot be omitted. But in any case, the titling of English Misplaced Pages articles relating to intellectual developments in Islamic countries is controversial. Therefore, if you want to propose a change to the title of this article, you must follow the appropriate procedure.
David Wilson (talk · cont) 13:42, 30 July 2013 (UTC)
Moving pages without consensus is not good. Having an revert edit war is worse. I've now added move protection to the page. If you want to start a move discussion please follow the procedure at WP:RM.
There have been previous discussion on the name of the page:
Talk:Mathematics_in_medieval_Islam/Archive_1#Move_to_Islamic_mathematics_or_Mathematics_in_Medieval_Muslim_World
--Salix (talk): 13:30, 30 July 2013 (UTC)

Abuse of blockquote

The abuse of blockquote is not neutral. What interest is it to have commentaries such as "it's fantastic" or "an important contribution" or "it is not brillant". These are point of view. What is neutral is to say wich person made what and what was known before him. The rest is only glorification. And it is not allowed. Sincerely yours. Tranquil Pepere (talk) 12:39, 30 July 2013 (UTC) In his A History of Mathematics, Victor Katz says that:

A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry.

An important role was played by the translation and study of Greek mathematics, which was the principal route of transmission of these texts to Western Europe. Smith notes that:

The world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics... their work was chiefly that of transmission, although they developed considerable ingenuity in algebra and showed some genius in their work in trigonometry.

Adolph P. Yushkevich states regarding the role of Islamic mathematics:

The Islamic mathematicians exercised a prolific influence on the development of science in Europe, enriched as much by their own discoveries as those they had inherited by the Greeks, the Indians, the Syrians, the Babylonians, etc.

Morris Kline in his book "Mathematical Thought from Ancient to Modern Times" says :

Though the mathematical work of the Hindus and Arabs was not brilliant ...

:

  1. Katz 1993. sfn error: no target: CITEREFKatz1993 (help)
  2. Smith 1958, Vol. 1, Chapter VII.4. sfn error: no target: CITEREFSmith1958 (help)
  3. Sertima, Ivan Van (1992), Golden age of the Moor, Volume 11, Transaction Publishers, p. 394, ISBN 1-56000-581-5
  4. Mathematical Tought from Ancient to Modern Times, Vol.1, Morris Kline, Oxford University Press, 1972, page 197

Exemple of disinformation

Al-Biruni developed a new method using trigonometric calculations to compute earth's radius and circumference based on the angle between the horizontal line and true horizon from the peak of a mountain with known height.

This is an example of disinformation I have suppress. There is no interest to evoke the second person who have discovered something. And the manner it was introduced let us presume that Al-Burini has calculated for the first time the radius of the earth. He was the second one.

Eratosthenes of Cyrene calculated the circumference of the Earth and obtained 250,000 stadia}} (it is believed that a stadium was 157 meters). So the result of Erathostene is 24,662 miles

  1. Mathematical Thought from Ancient to Modern Times, Volume 1, Morris Kline,p.161


— Preceding unsigned comment added by Tranquil Pepere (talk • contribs)

There is no disinformation in the quoted passage about Al-Biruni's calculation of the Earth's radius. You have simply missed the point of it entirely, which is that Al-Biruni was the first person known to have calculated the Earth's radius using the method described. That method is completely different from the one used by Eratosthenes, and is potentially much less expensive to apply, in that it doesn't require one to carefully measure the distance between two points some 100 or more km apart (in fact, about 900km in Eratosthenes's case). As it happens, the method isn't very useful in practice because the effect of atmospheric refraction on the measurements is not accurately determinable, but that doesn't make it entirely uninteresting.
David Wilson (talk · cont) 17:19, 30 July 2013 (UTC)
He is the second to have calculated the Earth radius. He is not a notable person for that. What's the interest to be the second. You violate the rules if edition. John Doe was the millionth to solve a second degree equation. What's the interest for that. Sincerly.Tranquil Pepere (talk) 10:04, 6 August 2013 (UTC)

Translation of French Misplaced Pages

Arithmetic

Irrationnals numbers

Magnitudes and irrationals

According to Kline,

If Euclid had really offered a theory of irrationals

, there are twa possible interpretations :

the first is that magnitudes themselves could be taken to be the irrational numbers, and the second is that the ratios of two magnitudes could be the irrational numbers

The use of irrationnals

Babylonians used tables of cibic and square roots, providing accurates approximations like √2 = 1,414213… · . The discovery of irrationnal numbers was made by Hippasus of Metaponto (V th century). The proof of the irrationality of √2 was made by Pythagorus using an "ab absurdo" demonstration · . Theodorus of Cyrene has proved the irrationality of √3, √5 and √7. Theaetetus realised a first classification of irrationnal numbers . Euclides analysed all the possibilities for lines that could be mathematizied by a + b {\displaystyle {\sqrt {{\sqrt {a}}+{\sqrt {b}}}}} (a et b are lines). Romans of Alexandria, at the opposite of the Greek who did not recognize the irrationals like numbers, used them like numbers for measuring the lenght, the area and the volume. Hindus (200-1200) used correct operations with irrational numbers, like addition and substraction. The principle is : a + b = ( a + b ) + 2 a b {\displaystyle {\sqrt {a}}+{\sqrt {b}}={\sqrt {(a+b)+2{\sqrt {ab}}}}} . The persian mathematician Omar Khayyam (1048-1122) stated that all ratio of measure, rational or irrational, could be named a number. The Arabs copied the operations on irrationals introduced by Hindus. One must wait until the XVIIIth century to have a good survey of irrational numbers. In 1727, Bernard le Bovier de Fontenelle stated that

the irrational numbers are proportionnaly more and more important that rationnal

Inside the work of synthesis made by Arabs, was Abu Kamil who used the irrationnal numbers and Al-Karaji. Another arab mathematician of the IX th century, Tabit ibn Qurra who translated greek manuscripts but was also studying the friendly numbers.

Positional numeration

In the twelfth century, Latin translations of Al-Khwarizmi's Arithmetic on the Indian numerals introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources. He revised Ptolemy's Geography and wrote on astronomy and astrology.

In 628, the Hindu astronomer and mathematician Brahmagupta published Brahma Siddhanta, treaty where he exposed a decimal numeration exactly the same that we use today. The numération positionnelle indienne was copied by arab mathematician.

The positional zero indicating a missing cipher

The positionnal zero was used for the first time by Babylonians during the Seleucid period the take over by the Greeks during Alexandrian period. They used different symbols for the representation of the positional zero comme : 0 ¯ {\displaystyle {\overline {0}}} . The arab mathematician copied the idea.

The zero as number

Hindus treated the zero as a number. The hindu mathematician announced that the multiplication of a number by zero is equal to zero and that substract zero do not diminish a number. According to him, to divide a number by zero maintain this number unchanged · . The arab mathematiocian copied the hindu model.

Calculus of Pi

The persian astronomer and mathematician Al-Kashi calculated an approached value of π. Archimedes has calculated 3 decimals.

Algebra

The attribution to Diophantus of the origin of algebra is discuussed since the Renaissance. According to Jens Høyrup,

Al-Khwarismi informe us that he has not create this branch of mathematics

 · . He quote, giving strenght to his argumentation, the passage of '"Al-Gabr w'al-muqabala" where Al-Khwarismi refers to "arithmetics used by a notary sollicitor" · . According to him

Al-Kwarismi only poduced a synthesis work of disciplines and algorithm, including the genuine superstructure

 ·  · . This synthesis work will play a role during the Renaissance · .

Resolution of a system of equations

Diophantus solved equations with multiples unknows reducing the system to one unknown and solved it. Al-Khwarismi copied the method. According to Kline, the rab algebra is only rhetorical and was a backstep if we copare it to indian algebra and to Diophantus's algebra..

Equation of second degree

The resolution of second degree equation was well-known since Babylonians. Al-Khwarismi only explained the algebraic process by geometry.

The second treaty, Kitab fi'l-jabr wa'l-muqabala expose only operations on equations. He propose the resolution of second degree equation by a completion of squares.

Using of latin letters to represent the unknowns

Diophante used the first letter of a word state that it is a quantity, i.e. s {\displaystyle s} for side and even s 2 {\displaystyle s^{2}} to represent what he called the "power" of this quantity. Al-Khwarismi used the same words and the same sympbolic.

Using of x to represent the unknown

Many arab books use the x to represent the unknown. Given the great destruction of books of mathematics during "autodafés" (this of general Amr but also this of the "vanity butcher" ofSavonarole), one cannot say precisely wich mathematician (he could be also greek, indian or arabic) who used for the first time the x to represent the unknown. According to the well-known group of mathematicians Nicolas Bourbaki,

Diophante uses, for the first time, a litteral symbol to represent the unknown

 ·

Geometry

The property of plane geometry were well-known since Euclides (Books XI and XIII from Eléments). These properties were used by Arabs to develop pavements. The deutch artist Esher used mathematics in his work and was interested by zellige after having visit the Alhambra in 1936.

Trigonometry

The founder of trigonometry is Hipparchus. The division of the circonference of a circle in 360 degrees is dued to Hypsicles of Alexandria. Hipparchus calculated the number of units for a chord corresponding to a given number of degrees, and that's the same of our sinus function · . Menelaus (98 A.D.) déveloped the greek trigonometry in his books "Sphaerica" and "Chords in a circle" where one can find the concept of spherical triangle. His book "Sphaerica" has been translated in arab. The trigonometry was continued by Hindus. The astronomer and mathematician Al-Battani copied the works realised before and uses the sinus function and tangente function in astronomy and wrote tables to calculate them. The spherical trigonometry is dued to chinese mathematician Kuo Chou-tching (1231-1316) who created the chou-chih calendar.Tranquil Pepere (talk) 09:56, 6 August 2013 (UTC)

  1. Mathematical Thought from Ancient to Modern Times, Volume 1, page 72, Oxford University Press, 1972
  2. According to Kline 1972 harvnb error: no target: CITEREFKline1972 (help), one cannot say if Babylonians were aware of the existence of an infinity of decimals or sexagesimals for the irrationnal numbers or if they believed they can convert them in a finite number of sexagesimal if they have more place in the board they used.
  3. Kline 1972, p. 8 harvnb error: no target: CITEREFKline1972 (help).
  4. Kline 1972, p. 32 harvnb error: no target: CITEREFKline1972 (help).
  5. Reductio ad absurdum.
  6. ^ Kline 1972, p. 33 harvnb error: no target: CITEREFKline1972 (help).
  7. qualified often by Alexandrians, greek mathématicians belonging to the Roman Empire
  8. Kline 1972, p. 104 harvnb error: no target: CITEREFKline1972 (help).
  9. ^ Kline 1972, p. 185 harvnb error: no target: CITEREFKline1972 (help).
  10. Kline 1972, p. 191-192 harvnb error: no target: CITEREFKline1972 (help).
  11. ^ Kline 1972, p. 192 harvnb error: no target: CITEREFKline1972 (help).
  12. (French) les nombres irrationnes se trouvent en une quantité sans comparaison plus grande que les nombres rationnels
  13. Jean Mawhin, Analyse, fondements, technique, évolution, De Boeck Université, Bruxelles, 1992, 1st édition, p. 38.
  14. Struik 1987, p. 93 harvnb error: no target: CITEREFStruik1987 (help)
  15. Rosen 1831, p. v–vi harvnb error: no target: CITEREFRosen1831 (help); Toomer 1990 harvnb error: no target: CITEREFToomer1990 (help)
  16. Corbalan, Fernando (9 2011). Le Nombre d'or: Le langage mathématique de la beauté. 1. Translated by Youssef Halaoua, Maguy Ly et Laurence Moinereau. RBA-Le Monde. p. 18. {{cite book}}: Check date values in: |date= (help).
  17. Kline 1972, p. 132 harvnb error: no target: CITEREFKline1972 (help).
  18. Today, mathematicians say that to divide a number by zero is equal to multiply it by infinity.
  19. G. Cifoletti, La question de l'algèbre. Mathématiques et rhétorique des hommes de droit dans la France du Template:XVIe siècle, Annales, 1995, vol. 50, p. 1385-1416, Template:Lire en ligne.
  20. « Algèbre d'al-ğabr » et « algèbre d'arpentage » au neuvième siècle islamique et la question de l'influence babylonienne, Fr. Mawet et Ph. Talon, D'Imhotep à Copernic. Astronomie et mathématiques des origines orientales au moyen âge. Actes du Colloque international, Université Libre de Bruxelles, 3‑4 novembre 1989. (Lettres Orientales, Leuven, Peeters, 1992 , p. 88.
  21. (French) Al-Khwarismi nous informe qu'il n'a pas inventé la discipline
  22. The algebra and the algorithms of calculus
  23. (French) arithmétiques utilisées constamment dans les affaires d'héritage et de legs
  24. Translation of Sayili, 1962.
  25. (French) al-Khwarismi n'a fait "que" produire une oeuvre de synthèse des disciplines et techniques des calculateurs pratiques, y compris la superstructure "pure"
  26. By superstructure, one can understand problems encoutered during professional life and the skill to solve them. Genuine refers to genuine mathematics or scientific mathematics used by Greek. (Summary of a note of Høyrup 1992, p. 89 harvnb error: no target: CITEREFHøyrup1992 (help)).
  27. Cite error: The named reference Hoyrup88 was invoked but never defined (see the help page).
  28. Høyrup 1992, p. 108 harvnb error: no target: CITEREFHøyrup1992 (help).
  29. The auteur say also that this role is probable concerning Cardan, but may be also to Viète.
  30. Kline 1972, p. 193 harvnb error: no target: CITEREFKline1972 (help).
  31. The name of this mathematician, latinised in Algoritmi, gived the word algorithm.
  32. (French) Livre sur la restauration et la confrontation
  33. Like in the book Farhenheit 351
  34. Nicolas Bourbaki, Éléments d'histoire des mathématiques, Masson, Paris, 1994, 3rd tirage, p. 69.
  35. The authors insinuate that Diophantus has created the x in mathematics because they don't quote any arab mathematician in the chapter devoluted to algebra.
  36. Kline 1972, p. 85-86 harvnb error: no target: CITEREFKline1972 (help).
  37. Corbalan 2011, p. 81 harvnb error: no target: CITEREFCorbalan2011 (help).
  38. ^ Kline 1972, p. 119 harvnb error: no target: CITEREFKline1972 (help).
  39. The circonference is divided in 60 parts, each part is divided in 60 parts of parts. The diametra is divided in 120 parts.
  40. La corde est le double du côté d'un triangle rectangle inscrit dans un quadrant de cercle et ayant comme rayon l'hypothénuse. Un côté de l'angle droit d'un triangle rectangle est égal au produit de l'hypothénuse par le sinus de l'angle opposé.
  41. ^ Kline 1972, p. 120 harvnb error: no target: CITEREFKline1972 (help).
  42. According to Kline 1972, p. 195 harvnb error: no target: CITEREFKline1972 (help), The Arabs made very little progress in astronomy.
  43. Philip J.Davis et Reuben Hersh, L'univers mathématique, translated in french by L. Chambadal, Gauthier-Villars, 1985, p. 26.
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