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Fibonnaci was no exception, in Bijaya

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Abudhar View Drop Down

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  Quote Abudhar Quote  Post ReplyReply Direct Link To This Post Topic: Fibonnaci was no exception, in Bijaya
    Posted: 18-Jun-2013 at 09:45



Once upon a time,Bijaya or Bejaia(Eastern Algeria)  was the Learning Centre of Europeans,Fibonnaci was no exception


*It would be important at first to mention that the city of Bejaia or Bijaya is a city on the eastern Algerian coast, built in an amphitheatre around a bay, sheltered from the sea elements. Al-Bakri's description of the city tells that it was a very ancient town inhabited by Andalusians and having a good harbour suitable for wintering in.


*Bejaia or Bijaya  witnessed great changes under the Hamadites in the eleventh century ,travellers praised its wealth and magnificence , Al-Idrisi wrote: it  is the capital of the Banu Hammad, ships unload there, caravans come to it by land and it is a depot for merchandise , at the same time ,merchants of this town trade with those of Western Africa as well as with those of the Sahara and east, merchandises of all sorts may be found here. The surrounding mountains and valleys are well wooded and produce resin and tar of excellent quality so that large ships for war and commerce are built here.

*Iver sums up perfectly the two main functions which made the renown of the city Learning was held in honour as well as the pursuit of industry and commerce, while the two, as will be shown further on, will eventually combine to produce one of the greatest manifestations in the history of science: the beginning of modern Western mathematics.

*First, business wise, just like the Hammadites before them, the Almohads (in the twelfth century forward) maintained excellent trade partnerships with the Italian cities, especially with Pisa.Christian merchants had funduqs (hotels)in Bejaia and came to buy wool, oil, hides, and wax, moreover,the Genoese were establishing themselves in North Africa, but especially at Bejaia, they were exporting products which they had themselves imported, such as cotton, linen and indigo, while Bejaia, on her part, was exporting to Genoa products which she also imported such as alum, wax and gold.


*There is some evidence from Arabic sources that alum was reaching Bejaia and the North African posts by caravans across the Sahara, which illustrates the great intricacy of early trade relationships in the Mediterranean, with regard to learning, at some point of its  history, Bejaia had become one of the most learned cities in Africa.

A contemporary had left an account of the years 1203-1299, called The gallery of men of literature of Bejaia of the seventh century of Hijra, which include large numbers of doctors, jurisprudence experts, mathematicians, and poets.


*The historian Al-Ghubrini, himself a native of Bejaia, gives the biography of 140 personages illustrious for their knowledge or piety who lived in the city, amongst whom can be mentioned the scholars of Islamic law (fakihs): Omara Ibn yahia l'Hussaini, Abdallah b. Omar al-Kaisi, the historians: Muhammad b. al-Hassan B. Maimun, physicians such as Ahmad B. Khalid, Taki al-Din of Mosul, and of course the famed Ibn Tumart, who appeared in Bejaia as a preacher ,Sarton also refers to Ibn Hammad, a Maghribi chronicler, who was born at Bu-Hamra c.1150; and who studied at the Qala'a of the Banu Hammad nearby, then in Bejaia and other places. He wrote a chronicle of Bejaia, and in 1220 a brief account of that convulsed period corresponding to the disintegration of Muslim unity in North Africa, and coinciding with Fatimid rule in Africa (909-1171): Akhbar muluk Bani Ubaid wa siratuhum (accounts on the rulers of Banu Obaid, and their deeds). In spite of its brevity that account is valuable because it is one of the earliest and contains first hand references to local conditions.

*North Africa, and Bejaia, like Fez and Marrakech, was remarkable for mathematical knowledge, above all. And one of the city's most illustrious mathematicians was by the name of al-Qurash, a scholar, who was a native of Seville, and who lived and died in Bejaia in 1184. The biographers who evoked him consider him a specialist in Algebra and in the Science of Inheritance calculations (next to his specialisation in certain religious sciences).


*In Algebra, al-Qurash is known for his commentary on the book of the great Egyptian mathematician Abu Kamil (d. 930). This commentary has not yet been recovered but its importance is confirmed by the historian Ibn Khaldun who considered it one of the best treaties written on the book of Abu Kamil, and this is the judgment of somebody who knows because Ibn Khaldun had an excellent mathematical education, and one even attributes him a youth of writing on this discipline.


*In relation to the content of the treatise of al-Qurash, this was not a simple commentary on a famous treatise of algebra of its time. One finds here indeed some new elements, first of all, at the level of presentation, since al-Qurash starts by presenting the objects and the operations of Algebra before explaining the solution of the canonical equations followed by the demonstration of the existence of the solutions of these equations.


*In these two chapters, one remarks that al-Qurash distinguishes himself from his predecessors in the classification of the six canonical equations and in the demonstrations,this work continued to be studied and taught in the Maghrib until the 14th century, as confirmed by Ibn Zakariya. One may even suppose that it is the importance of this book that led Ibn al-Banna (d. 1321) to write, some decades later, his Kitab al-usous wa l-muqaddim fil-jabr [Book of the foundations and of the preliminaries in Algebra].


*In the domain of inheritance, al-Qurash is known for having elaborated a new method based on the decomposition of the numbers in prime factors in order to reduce the fractions that intervene in the distribution of a given inheritance to the same denominator,his method was very quickly appreciated by the mathematicians who wrote the handbooks explaining it and by showing its usefulness through the presentation of concrete problems of inheritance.


*Business and mathematics coming to the fore form Bejaia, but in a more dramatic and lasting manner: that it is a city impacting the whole of Western mathematics, and the whole of science, in fact.

Bejaia: From a Trading Centre to acting as the Source of Western Mathematics:

*Bejaia symbolises something extraordinary, that is the marriage between business and science, and it came via the Italian city of Pisa, one of the major trading powers of the Middle Ages, and soon the birth place of modern Western mathematics. The Republic of Pisa had two permanent consuls in the African kingdoms, one residing in Tunis, and the other in Bejaia, thus,the Pisans were seen as old friends,they had a quarter or specific funduqs, comprising many houses and surrounded by walls; they worked in all security, and practiced for a long time imports and exports.

*The position they had given to them are obvious in a letter sent by the emir to the Archbishop of Pisa, chief of the government of the republic, as such in  1133, a delegation of Almoravid high dignitaries travelled to Pisa and signed with the Republic a major treaty; Pisa, then had in the Mediterranean a maritime presence that Amalfi and Naples had lost, Just as in Tunis, in Bejaia, the Pisan traders owned houses and shops (magasins) distinct from the large funduqs of the nation, near which could be cited the cemetery and the Church or chapel. Independently from the consul and his employees, and other legal officials, each nation had a special official, or a Christian book keeper, called the scriber , he was summoned to register the merchants' accounts of his country to present to the Muslim duana (Customs), and also watch for his compatriot interests. One of these scribes was a certain Bonacci. It is with his father, the scribe of the Pisan nation at the Duana of Bejaia, at the end of the 12th century, that the famed mathematician Leonardo Fibonacci learnt the principles of arithmetic, algebra and geometry, In his contacts with Muslim traders, the father had, indeed, realised the superiority of Arabic numerals, and to prepare his son (Leonardo) for running the family business, he sent him to a Muslim teacher of mathematics in Bejaia.

Location of Bejaia

*Fibonacci praises the sort of learning he received in Bejaia in the 1228 edition of his famous Liber Abbaci (also spelt Liber Abaci):

'After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvellous instruction in the artâa ,the knowledge of the art very much appealed to me before all others , I pursued my study in depth and learned the give-and-take of disputation,.I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things.


*Not only was Fibonacci the first to explain Muslim arithmetic but his works, especially his later ones, contain many original ideas, His Liber Abaci of 1202 may be called the first monument of European mathematics,his second edition of the Liber Abaci, which would finally establish the 'Andalusian' number system as the basis of modern mathematics, would be dedicated to Frederick II, the then great emperor of southern Italy, and the great promoter of scientific learning in the Christian West. Frederick, just like Fibonacci shared the same respect for Islamic culture.

*Both had been impregnated since childhood by a dominant Islamic culture, one in Palermo and the other in Bejaia, and both had Muslim teachers, one spoke the language, and the other understood elements of it, So crucial was Fibonacci's contribution, that as Sarton notes, the mathematical renaissance in the West may be dated to him.

*Liber Abaci shows indisputable filiations with Islamic precedents, concerning the types of problems addressed; the methods for their solution; terminology, and even symbolism , indeed, Liber Abbaci became a landmark of European mathematics, and Fibonacci's arithmetic was, eventually, propagated to Europe by such writers as Villedieu and Sacrobosco , this until the 16th century at least, generations of mathematicians did not cease relying on Fibonacci's writing.

The End of the Great Role of Bejaia

The prosperity of Bejaia went on under the Almohads, who also prevented the city form falling under Norman hands, the Normans who then had taken much of Tunisia, and were extending their realm, threatening the suppression of Islam in the whole of North Africa,indeed, in 1148, Al-Mahdiya fell to the Normans; so did Susa; Sfax; soon after the conquest of al-Mahdiya. The dominion of the Normans extended from Tripoli to the borders of Tunis, and from the western Maghrib to Qayrawan showing the strength of victors, the  Normans sought to extend their dominion westwards as far as Bejaia, another terminal of the trans-Saharan route, and possibly at this time a more prosperous centre than Al-Mahdiya or Tripoli.


* The Almohads, so much hated by Western historians, saved the whole of North Africa from this fate, yet Muslim power was dwindling away, and Christian pirates terrorised the shores of the Muslim coast, from Morocco to as far as the Indian Ocean , at that time of history, the inhabitants of North Africa were, indeed, under constant threat of attacks by European pirates, who often came disguised as Muslims in order to capture Muslims, and sell them as slaves for the galleys.


*Ottoman  seamen used those southern shores to rest between their expeditions to the north and to the West, and often wintered in one of the harbours or islands, and one of their seamen, Piri Reis described the place just prior to the Spanish invasion , he went on to describe Bejaia favourably, that it was a handsome fortress situated on a pine tree covered mountain slope with one side on the shore. The city's ruler was called Abdurrahman, related to the Sultan of Tunis, a family descendant from Caliph Ommar Ibn al-Khatab (634-644).


*He observes that among all the cities of the Maghreb, none would offer a spectacle comparable to it, Piri Reis must have seen the Hammadite palaces and was so impressed by them before they were destroyed by the Spaniards when they took the city in 1510, The Spaniards forced the population to flee to the mountains, settled part of it, and razed the rest , left to its sorrowful  fate , Bejaia was to be retaken forty five years later, in 1555 by Salah Reis, Beylerbey of Algiers.


*The Spaniards, however, had so harmed the city that it was never able to recover its former prosperity , with the French colonisation that stated  in 1830 and the French naval heavy bombardment of 1833 devastated the city before it was forced to surrender to them and despite the destruction and heavy casualties, the resistance against the French by the inhabitants of Bejaia never lessened, and many times the French were on the verge of evacuating the city, and when the war of independence (1954-62) took place the region of Bejaia was at the forefront of anti French resistance.

*Bejaia illustrates for us the important role trade relations had between Europe and the Muslim world,evenhrough true to say that Islamic civilisation interacted extensively with European Civilisation, not through war but on the basis of peaceful mutual enrichment, this was easily demonstrated throughout the ages and specially within this survey, which in time we value far more than mere perishable goods, it involved substantial transfer of knowledge.


*Sources and Bibliography:

-D. Abulafia: The Norman Kingdom of Africa and the Norman Expeditions to Majorca and the Muslim Mediterranean; in D. Abulafia: Italy, Sicily and the Mediterranean 1100-1400; Varorium Reprints; London; 1987; pp. 27-49.

-Al-Bakri: Description de l'Afrique; Trans. De Slane.

-Cahiers du Seminaire Ibn al-Haytham; Algiers; 1995; 1996.

-M. Cherbonneau: Gallerie des Litterateurs de Bougie au septieme siecle de l'Hegire; Revue Algerienne et Coloniale; Paris; June 1860.

-M.L. de Mas Latrie: Traites de paix et de Commerce, et Documents Divers, Concernant les Relations des Chretiens avec les Arabes de l'Afrique Septentrionale au Moyen Age, Burt Franklin, New York, Originally Published in Paris, 1866.

-A. Djebbar: Quelques elements nouveaux sur les activites mathematiques arabes dans le Maghreb Central (IX-XVI em siecles) Second Maghrebian Coloqium on the history of Arabic mathematics; Tunis; 1-3 December 1988.

-A. Djebbar: Enseignement et Recherche mathematiques dans le Maghreb des Xiii et XIV siecles; paris; University of Paris Sud; Publications Mathematiques d'Orsay; No 81-2; 1980. pp. 8-10.

-A. Djebbar: Les Activites dans le Maghreb Central (XII et XIX siecles; 3rd Maghrebian colloqium on the history of mathematics; Algiers; 1-3 December 1990.

-A.Djebbar: Une Histoire de la Science Arabe; Le Seuil; Paris; 2001.

-P. Earle: Corsairs of Malta and Barbary; London; 1970.

-R.E. Grimm: The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, 1973, pp. 99-104.

-Al-Idrisi: Trans by de Goeje and Dozy.

-G. Iver: Bougie; Encyclopaedia of Islam; vol 1; first series; pp. 766-8.

-C. A. Julien: Histoire de l'Algerie Contemporaine, 1827-1871: Presses Universitaires de France, 1964.

-Ibn Khaldun: Al-Muqaddima; Beirut; Dar al-Kitab; Vol 1.

-J. Mathiex: Trafic et prix de l'Homme en Mediterranee au 17 et 18 Siecles; ANNALES: Economies, Societes, Civilisations: Vol 9:pp 157-164.

-Maria Rosa Menocal: The Arabic Role in Medieval Literary History, University of Pennsylvania Press, Philadelphia, 1987.

-R. Rashed: Fibonacci et les mathematiques Arabes, pp 145-160; in Micrologus: Nature, Sciences and Medieval societies, II. 1994: Science at the Court of Frederick II. Brepols,1994.

-G. Sarton: Introduction to the History of Science; The Carnegie Institute; Washington; 1927.

-C. Singer: The Earliest Chemical Industries; The Folio Society; London; 1958.

-S. Soucek: Tunisia in the Kitab-I Bahriye of Piri Reis, Archivum Ottomanicum, Vol. 5, pp 129-296.

-W. Montgomery Watt: The Influence of Islam on Medieval Europe, Edinburgh University Press, 1972.


















Edited by red clay - 18-Jun-2013 at 10:54
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red clay View Drop Down
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  Quote red clay Quote  Post ReplyReply Direct Link To This Post Posted: 18-Jun-2013 at 10:57
Abudhar, I edited your post.  There is no reason for having the type face at 7.  At least you have provided sources.
I wish others here would learn from you. Thank you.
"Arguing with someone who hates you or your ideas, is like playing chess with a pigeon. No matter what move you make, your opponent will walk all over the board and scramble the pieces".
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  Quote toyomotor Quote  Post ReplyReply Direct Link To This Post Posted: 03-Feb-2014 at 20:55
Originally posted by red clay

Abudhar, I edited your post.  There is no reason for having the type face at 7.  At least you have provided sources.
I wish others here would learn from you. Thank you.

Red: For my enlightenment, what use is the Fibonacci except in perhaps pure mathematics or physics?
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