1. References For Al-Banna References for ibn albanna. Arabic Sci. 6 (1-2) (1982), 278-209. HPJ Renaud, Ibnal-Banna de Marrakech, sufi et mathématicien, Hesperis 25 (1938), 13-42. http://www-gap.dcs.st-and.ac.uk/~history/References/Al-Banna.html

References for Ibn al-Banna Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: R Rashed, The development of Arabic mathematics : between arithmetic and algebra (London, 1994). R Rashed, (Paris, 1984). Articles: (Algiers, 1988), 133-156. Histoire de fractions, fractions d'histoire (Basel, 1992), 247-258; 405-406; 411. G Arrighi, Review of some mathematical symbols (Italian), Physis - Riv. Internaz. Storia Sci. A Djebbar, (Orsay, 1981). R Rashed, Materials for the study of the history of amicable numbers and combinatorial analysis (Arabic), J. Hist. Arabic Sci. Hesperis Isis Arabic Sci. Philos. M Zarruqi, Fractions in the Morroccan mathematical tradition between the 12th and 15th centuries A.D. as found in anonymous manuscripts (Arabic), in (Tunis, 1990), A97-A109. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Al-Banna.html

2. History Of Mathematics: Arabic Mathematics Khalili (c. 1250); ibn albanna (1256-1321); Ghiyath al-Din al-Kashi(d. 1429); Ulugh Beg (1394-1449). Sources. Library of Congress Vatican http://aleph0.clarku.edu/~djoyce/mathhist/arab.html

Arabic Mathematics This page is under development. Mathematicians Banu Musa (sons of Musa ibn Shakir) (ninth century) al-Hajjaj ibn Matar (c. 800) Muhammad ibn Musa Al-Khwarizmi (c. 780-c. 850) Hunayn ibn Ishaq (Johannitius) (808-873) `Abd al-Hamid ibn Turk (c. 850) Ahmad ibn `Abdullah al-Marwazi Habas al-Hasib (c. 850) Thabit ibn Qurra (836 -901) al-Fadl al-Nayrizi (c. 880) Abu Kamil ibn Aslam (c. 850-930) Qusta ibn Luka (d. 912) Abu `Abdallah Mohammad ibn Jabir al-Battani (Albatenius) (c. 858-929) Abu Nasr al-Farabi (Alpharabius) (c. 878-c. 950) Ibrahim ibn Sinan (909-946) Abu Sahl al-Kuhi (c. 950) Abu l'Hasan al-Uqlidisi (c. 952) `Abd al-`Aziz al-Qabisi (c. 950) Muhammad Abu l'Wafa (Albuzjani) (940-998) Abd al-Jalil al-Sijzi (c. 970) Abu `Ali al-Hasan ibn al-Haytham (Alhazen) (c. 965-1039) Abu l-Rayhan Muhammad ibn Ahmad al-Biruni (973-1055) Abu Bakr al-Karaji (al Karkhi) (c. 1000) Abu `Abdallah al-Hasan ibn al-Baghdadi (c. 1000) Kushyar ibn Labban (c. 1000) Maslama al-Majriti (c. 1000) Abu Nasr Mansur ibn Iraq (d. 1030) Abu Mansur al-Baghdadi (c. 1025)

3. Al-Banna alMarrakushi ibn al-banna. Born 29 Dec ibn al-banna is also knownas Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi. It is a http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Al-Banna.html

al-Marrakushi ibn Al-Banna Born: 29 Dec 1256 in Marrakesh, Morocco Died: 1321 in Marrakesh, Morocco Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ibn al-Banna is also known as Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi. It is a little unclear whether al-Banna was born in the city of Marrakesh or whether it was the region of Marrakesh which was named Morocco by Europeans. There is a claim that al-Banna was born in Granada in Spain and moved to North Africa for his education. What is certain is that he spent most of his life in Morocco. Morocco was certainly the country that al-Banna was educated in, learning the leading mathematical skills of the period. He studied geometry in general, and Euclid 's Elements in particular. He also studied fractional numbers and learnt much of the impressive contributions that the Arabs had made to mathematics over the preceding 400 years. The Marinids had a strong culture for learning and Fez became their centre of learning. At the university in Fez Al-Banna taught all branches of mathematics, which at this time included arithmetic, algebra, geometry and astronomy. Fez was a thriving city with a new quarter being built housing the Royal Palace and the adjoining Great Mosque. Many students studied under al-Banna in this thriving academic community. It is clear that al-Banna wrote a large number of works, in fact 82 are listed by Renaud (see for example [9]). Not all are on mathematics, but the mathematical texts included an introduction to

4. Al-Banna ibn albanna is also known as Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi. http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Banna.html

al-Marrakushi ibn Al-Banna Born: 29 Dec 1256 in Marrakesh, Morocco Died: 1321 in Marrakesh, Morocco Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ibn al-Banna is also known as Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi. It is a little unclear whether al-Banna was born in the city of Marrakesh or whether it was the region of Marrakesh which was named Morocco by Europeans. There is a claim that al-Banna was born in Granada in Spain and moved to North Africa for his education. What is certain is that he spent most of his life in Morocco. Morocco was certainly the country that al-Banna was educated in, learning the leading mathematical skills of the period. He studied geometry in general, and Euclid 's Elements in particular. He also studied fractional numbers and learnt much of the impressive contributions that the Arabs had made to mathematics over the preceding 400 years. The Marinids had a strong culture for learning and Fez became their centre of learning. At the university in Fez Al-Banna taught all branches of mathematics, which at this time included arithmetic, algebra, geometry and astronomy. Fez was a thriving city with a new quarter being built housing the Royal Palace and the adjoining Great Mosque. Many students studied under al-Banna in this thriving academic community. It is clear that al-Banna wrote a large number of works, in fact 82 are listed by Renaud (see for example [9]). Not all are on mathematics, but the mathematical texts included an introduction to

5. îÏ×ÁÑ áÓÔÒÏÌÏÇÉÞÅÓËÁÑ üÎÃÉËÌÏÐÅÄÉÑ ibn albanna. (arab. syn arhitektora ); sobstvenno Abu-l- `Abbas Ahmad ibn Muhammadibn `Usman al-Azdi (ok. 1260, Marrakesh, Marokko - ok. 1320, tam zhe) - http://encyclopedia.astrologer.ru:8005/cgi-bin/guard/I/Ibn-al-banna.html

6. 1995 Quelques Aspects Des Maths D'Ibn Al-Banna De Marrakech (1256-1321). propose de découvrir quelques chapitres des oeuvres d'ibn albanna. La mise en parallèle des textes intégraux http://publimath.univ-lyon1.fr/biblio/IRO99015.htm

Informations Pratiques recherche Recherche Auteur(s) : IREM de Rouen Groupe Histoire des maths. Grt. Titre : Quelques aspects des maths d'Ibn al-Banna de Marrakech (1256-1321). Editeur : IREM de Rouen , Rouen, 1995 r BORDER=0 BGCOLOR="#50B050" HEIGHT=32> Informations Pratiques recherche Informations ... Recherche

7. îÏ×ÁÑ áÓÔÒÏÌÏÇÉÞÅÓËÁÑ üÎÃÉËÌÏÐÅÄÉÑ ashShakur. Ibn Abi-r-Ridzhal (988-ok. 1064) - musul'manskii astronom i astrologIbn al-Baz'yar - arabskii astrolog IX v. ibn al-banna (ok. 1260-ok. http://encyclopedia.astrologer.ru:8005/list_i.html

8. 1995 Quelques Aspects Des Maths D'Ibn Al-Banna De Marrakech (1256-1321). propose de découvrir quelques chapitres des oeuvres d'ibn albanna. La mise en parallèle des textes intégraux http://publimath.univ-lyon1.fr/bibliocomp/IRO99015.htm

Informations Pratiques recherche Recherche ... Fiche Auteur(s) : IREM de Rouen Groupe Histoire des maths. Grt. Titre : Quelques aspects des maths d'Ibn al-Banna de Marrakech (1256-1321). Editeur : IREM de Rouen , Rouen, 1995 Collection : IREM de Rouen R 105 Format : A4, 150 p. ISBN : Type : document pour la classe issue de travaux de groupe IREM (INRP, CRDP), Langue : Français, Support : papier Utilisation : enseignant Informations Pratiques recherche Recherche Recherche Recherche

9. Biography-center - Letter I I. 51 biographies ibn albanna, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Banna.html;ibn Ishaq Hunayn, www-history.mcs http://www.biography-center.com/i.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish I 51 biographies ibn al-Banna, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Banna.html ibn Ishaq Hunayn, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hunayn.html ibn Sina, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Avicenna.html ibn Tahir, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Baghdadi.html ibn Tibbon, Jacob www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tibbon.html ibn Yusuf Ahmed, www-history.mcs.st-and.ac.uk/~history/Mathematicians/Ahmed.html Ibrahim, ibn Sinan www-history.mcs.st-and.ac.uk/~history/Mathematicians/Ibrahim.html Ibrahim, Murad Jussuf Bey www.whonamedit.com/doctor.cfm/1518.html Ibsen, Henrik www.kirjasto.sci.fi/ibsen.htm Ickx, Jacky www.grandprix.com/gpe/drv-ickjac.html Iglesia, Pablo

10. Timeline Of Islamic Scientists 1258 ibn al-banna (Al Murrakishi), Azdi - Medicine, Mathematics. 1262(died) - Al-Hassan Al-Murarakishi - Mathematics, Astronomy, Geography. http://www.levity.com/alchemy/islam10.html

Timeline of Islamic Scientists These pages are edited by Prof. Hamed Abdel-reheem Ead Professor of Chemistry at Faculty of Science-University of Cairo Giza-Egypt and director of Science Heritage Center E-mail: ead@frcu.eun.eg Web site: http://www.frcu.eun.eg/www/universities/html/shc/index.htm Back to Islamic Alchemy Back to reference library Timeline of Islamic Scientists (700-1400) This chart depicts the lifes of key Islamic Scientists and related writers, from the 8th to the end of the 13th century. By placing each writer in a historical context, this will help us understand the influences and borrowing of ideas. (died) - Khalid Ibn Yazeed - Alchemy - Jabir Ibn Haiyan (Geber) - (Great Muslim Alchemist) - Al-Asmai - (Zoology, Botany, Animal Husbandry) - Al-Khwarizmi (Algorizm) - (Mathematics, Astronomy) - Al Balkhi, Ja'Far Ibn Muhammas (Albumasar) - Astronomy, Fortune-telling (died) - Al-Fazari,Ibrahim Ibn Habeeb - Astronomy, Translation - Ibn Ishaq Al-Kindi - (Alkindus) - (Philosophy, Physics, Optics) - Hunain Ibn Is'haq - Medicine, Translator

11. Do You Know This Famous Moroccan? - Www.ezboard.com this famous Moroccan? His name is ibn albanna is also known as Abu'l-AbbasAhmad ibn Muhammad ibn Uthman al-Azdi. It is a little http://pub14.ezboard.com/fmoroccofrm18.showMessage?topicID=20.topic

12. Al-Qalasadi Biography of AlQalasadi (1412-1486) and, perhaps to some extent following the example of ibn al-banna, al-Qalasadi followed it up by writing a simpler http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Al-Qalasadi.html

Abu'l Hasan ibn Ali al Qalasadi Born: 1412 in Bastah (now Baza), Spain Died: Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Al-Qalasadi (or al-Kalasadi, as it is sometimes written) was born in Bastah, a Moorish city in Andalusia, now a part of Spain. Andalusia was derived from the Arabic name al-Andalus which was originally applied by the Muslims to the whole of present day Spain and Portugal, an area which they occupied from the 8th century. In the 11th century Christians began to retake the area, slowly moving down from the north and east. Andalusia was then the name applied to the region remaining under Muslim rule. The Christian reconquest took four hundred years. Andalusia had prospered during the 13th century and the Alhambra, a wonderful palace and fortress of the rulers of Granada, was largely completed by 1360. The Christian kingdom of Castile to the north had suffered civil strife through the 14th century, so Andalusia had prospered but, in 1407, five years before al-Qalasadi was born, Castile began a major push to conquer the whole of Spain and Portugal. Al-Qalasadi was a Muslim who was brought up in Bastah which is north-east of Granada city. It must have been a difficult period in which to live in Bastah, with a steady, yet intermittent, encroachment of Castile towards the city. Al-Qalasadi began his education in Bastah, studying law, the Qur'an and the science of fixed shares in an estate. He moved south, away from the war zone, to Granada where he continued his studies, in particular philosophy, science and Muslim law.

13. History Of Mathematics: Chronology Of Mathematicians A list of all of the important mathematicians working in a given century.Category Science Math Mathematicians Directories...... Maximos Planudes (c. 12551310); ibn al-banna al Marrakushi (1256-1321)*SB; John Duns Scotus (c. 1266-1308) *SB; Peter Philomena of Dacia (fl. http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

14. Al-andalus Translate this page ibn al-banna était un mathématicien Marocain qui était mort 100 ans avant queAl-Qalasadi n’avait écrit son commentaire mais, peut-être c’est étonnant http://membres.lycos.fr/andalus/savants/Alqalasadi.htm

Dates importantes Début de l'histoire Omeyyades d'Espagne Emirs Omeyyades ... Effondrement Al-Qalasadi Abou Al Hassan ibn Ali Al Qalasadi ( né en 1412 à Bastah (Baza), Espagne mort en1486 à Béjaya, Tunisie Al-Qalasadi (ou Al-Kalasadi , comme il est écrit quelquefois) est né à Bastah , une ville Morisque dans l’Andalousie, maintenant une partie d'Espagne. L’Andalousie dérive du nom Arabe al-Andalouss qui a été appliqué originairement par les musulmans à la totalité de l’Espagne et le Portugal, une région qui avait appartenu à l’empire Islamique du 8 ième siècle. Dans le 11 ième siècle les chrétiens ont du à reprendre la région, se déplaçant lentement du nord et de l’est. L’Andalousie était alors le nom appliqué à la région restant sous le règne Musulman. La reconquête chrétienne avait pris quatre cents années. L’Andalousie avait prospéré pendant le 13 ième siècle et l' Alhambra , était un merveilleux palais et forteresse des souverains de Grenada , avait été construit en grande partie en 1360. Le royaume chrétien de Castille au nord avait souffert d’un conflit civile en 14 ième siècle, donc l’Andalousie avait prospéré mais, en 1407, cinq années avant la naissance de

15. Al-andalus Translate this page Al-Qalassadi, Ibn-Rushd. Al-Wazzani, Ibn-Alawam. Al-Zahrawi, ibn al-banna. Averroes,Al-Umawi. Ibn Majid, Muhyi l'din al-Maghribi. Jabir ibn Aflah, Abd Rahman III. http://www.multimania.com/andalus

Dates importantes Début de l'histoire Omeyyades d'Espagne Emirs Omeyyades ... Galerie Photos Al-Idrissi Premier géographe arabe à pénétrer l'Europe de la Renaissance et héritier de plusieurs traditions cartographiques arabes, al-Idr is s i réalise une synthèse des travaux de ses prédécesseurs . Il est repris par les auteurs qui lui succèdent : le géographe arabe Ibn Sa'îd, de Grenade (mort en 1274) et Abû Fidâ, de Damas (mort en 1331) ont copié ses notices. L'historien Ibn Khaldûn (mort en 1406) assure de son côté avoir suivi l'exemple d'Idr is s i Une version tardive et simplifiée de l'œuvre, aurait été rédigée en 1192 sous le titre de : "Le petit Edrisi", résumé du grand Carte de Al-Idrissi Astrolabe La méditerranée Témoignage de Ibn jubayr Contribution scientifique ... Email ©2002 Al-Andalus

16. 5 Translate this page Ce livre, écrit en arabe, est centré sur un traité philosophico-mathématiquedu XIV e siècle du mathématicien maghrébin ibn al-banna (1256-1321) qui s http://www.ashm.ass.dz/cahier8f/conred8f.htm

5. Compte-rendus 5 . 1 . Mohamed ABALLAGH Raf c al-hijab c an wujuh a c mal al-hisab li Ibn al-Banna al-Murrakushi (721/1321) [Le lever du voile sur les opérations du calcul d’Ibn al-Banna de Marrakech], Fès, Publications de la faculté des lettres et sciences humaines-Zhar al-Mahraz, n°5,1994, 360 pp. Ce livre, écrit en arabe, est centré sur un traité philosophico-mathématique du XIV e siècle du mathématicien maghrébin Ibn al-Banna (1256-1321) qui s’était rendu célèbre, durant des siècles, grâce un petit manuel , intitulé le Talkhis a c mal al-hisab [L’Abrégé des opérations du calcul] dont le Raf c al-hijab se veut un commentaire. Ce sont d’ailleurs les critiques dirigées contre certains passages du manuel qui auraient motivé la publication du livre. Dans ce dernier, l’auteur reprend le contenu de la thèse qu’il a soutenue en 1988 a l’Université de Paris I, à l’exclusion de la traduction française du traité. On y retrouve en effet l’introduction (pp. 17-93), l’édition critique du traité basé sur huit manuscrits (pp. 189-317), la transcription mathématique moderne de son contenu (pp. 95-198), un index terminologique et une bibliographie générale. A cela, l’auteur a ajouté une présentation (pp. 7-16) et trois autres index pour les noms propres, les titres des ouvrages et les noms de lieux. L’introduction rassemble, sous trois rubriques essentielles, les résultats des investigations menées par l’auteur à la fois à travers les nombreuses publications consacrées à Ibn al-Banna et, surtout, à travers des sources inédites, biobibliographiques, mathématiques et philosophiques.

17. 6 ABALLAGH M. L’influence des écrits mathématiquesd’ibn albanna sur lesmathématiciens égyptiens de l’empire ottoman, Symposium sur Science http://www.ashm.ass.dz/cahier8f/collo8f.htm

6 . Colloques 6. 1. XXe Congrés International d’histoire des Sciences (Liège, Belgique, 20-26/12/1997). Les communications suivantes liées à l’histoire des mathématiques arabes ont été présentés: ABALLAGH M. : L’influence des écrits mathématiquesd’Ibn al-Banna sur les mathématiciens égyptiens de l’empire ottoman, Symposium sur Science, Technology and Industry in the Ottoman World (SU7). (Org.) A. Djebbar et B. Ihsanoglu. ANSARI, S.M.R: The Mathematicien Family of Ahmad Mamar and their Works, Special session of Section 3: Islamic science and technology in Arabic-speaking countries, Central Asia and India, Org.S.M.P. Ansari. BAGHERI, M. : Discovery of a New Letterof al-Kashi, Symposium Science and Technology in anciens and medieval Iran, (Org.) J.P. Hogendijk et M. Bagheri. BELLOSTA, A.: Quelques lectures arabes des Données d’Euclide. Symposium sur The East and the West (S.M.19), Org.: A. Allard, R. Rashed et C. Sasaki. BEN MILED, A.M.: Le Livre X des Eléments d’Euclide dans la tradition arabe, Symposium sur The East and the West (S.M.), Org.: A. Allard, R. Rashed et C. Sasaki. BERGGREN, J.L.: Minor Geometrical Works of al-Kuhi: a Historical and Mathematical Survey, Symposium Science and Technology in ancient and medieval Iran, (Org.) J.P. Hogendijk and M. Bagheri.

18. The Ritual Prayer Of The Emancipated In Shawwal provided by Shaikh ‘Abd alQadir al-Jilani, may Allah be pleased with him Thisreport was conveyed to us by Shaikh Abu Nasr Muhammad ibn al-banna’, on the http://www.sunnah.org/ibadaat/shawwal/uttaqa.htm

CONCERNING THE RITUAL PRAYER OF THOSE WHO ARE EMANCIPATED [FROM THE FIRE OF HELL] IN THE MONTH OF SHAWWAL [ salat al-’utaqa’ fi Shawwal Excerpted from Ghunya al-Talibin li-Tariq al-Haqq by Sayidduna Shaykh Abd al-Qadir Jilani (q). As for the ritual prayer of those who are emancipated [from the Fire of Hell] in [the month of] Shawwal [ salat al-’utaqa’ fi Shawwal ], we learn from a traditional report, transmitted [by a chain of reliable authorities] from Anas [ibn Malik]* (may Allah be well pleased with him), that Allah's Messenger (Allah bless him and give him peace) once said: "If someone performs eight cycles of ritual prayer [ raka’at ] in the month of Shawwal, either during the night or during the day-reciting in each cycle the Opening Sura of the Book [ Fatihat al-Kitab ] [one time] and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" fifteen times-and if, when he has finished performing his ritual prayer [ salat ], he glorifies Allah [ sabbaha ] seventy times, and invokes Allah's blessing upon the Prophet (Allah bless him and give him peace) seventy times by Him who sent me as a Prophet bearing the Truth [ bi'l-Haqqi Nabiyyan ], no servant [of the Lord] will perform this ritual prayer [

19. AMU CHMA NEWSLETTER #24 (6/25/99) (continued) ( 297 322). 8.1 On the History of Mathematics in Africa. 297 Aballagh, MohamedIntroduction à l'étude de l'influence d'ibn al-banna sur les mathématiques http://www.math.buffalo.edu/mad/AMU/amu_chma_24a.html

AMUCHMA-NEWSLETTER-24 (continued) BACK to Newsletter 24 first page TABLE OF CONTENTS (continued) Have you read? Announcements Addresses of scholars and institutions mentioned in this newsletter New recipients ... back to AMUCHMA ONLINE 8. HAVE YOU READ? 8.1 On the History of Mathematics in Africa #297 Aballagh, Mohamed: Science, Technology and Industry in the Ottoman World. , Brepols Publisher, Turnhout, 2000, Vol. VI, 75-80. The author presents information concerning the circulation of mathematics in the north of Africa through the example of three works of Ibn al-Banna. #298 Djebbar, Ahmed: Figurate Numbers in the Mathematical Tradition of al-Andalus and the Maghreb Suhayl , Barcelona, Vol. 1 (2000), 57-70. The paper analyses certain contributions made in Andalusia and the Maghreb to the theme of figurate numbers. These numbers are a geometrical representation of numbers and had been created by the Pythagorean School. The oldest known study of these numbers is found in the "Introduction to Arithmetic" by Nicomachus. A Arabic translation of this work circulated in Andalusia and in the Maghreb from the 10th century onwards. #299 Djebbar, Ahmed:

20. Culture Of Muslim Spain Also during the heyday of Granada, there was 'Ali alQalasadi, commentatoron ibn al-banna`, who did important work on fractions. http://lilt.ilstu.edu/bekurtz/culture.htm

Culture of Muslim Spain Arab civilization in the peninsula reached its zenith when the political power of the Arabs began to decline. In the 8th century, in the years immediately following the conquest, there were no traces of a cultural level higher than that attained by the Mozarabs who lived among the Arab conquerors. All available evidence points to the fact that in this period popular works of medicine, agriculture, astrology, and geography were translated from Latin into Arabic. Many of these texts must have been derived from the Etymologies of Isidore of Seville and from other Christian writers. In the 9th century, the situation changed abruptly: the Andalusians, who traveled east in order to comply with the injunction to conduct a pilgrimage to Mecca at least once in their lifetimes, took advantage of their stay in those regions to enhance their knowledge, which they then introduced into their native country. Literature. The highest peak in Islamic literature in Spain was attained during the era of the ta`ifas, when the poet-king al-Mu'tamid established an embryo of an academy of belles lettres, which included the foremost Spanish intellects as well as Sicilians who emigrated from their native land before its conquest by the Normans. Other petty kings in the peninsula endeavoured to compete with al-Mu'tamid but did not succeed in assembling a constellation of writers of comparable stature. Among the outstanding poets of the 12th century in eastern Andalusia (the Andalusian Levant) were Ibn Khafaja of Alcira and his nephew Ibn az-Zaqqaq. To the era of greatest decadence in the 13th century belonged Abu al-Baqa` of Ronda and Ibn Sa'id. In the 14th century three court poets, Ibn al-Jayyab, Ibn al-Khatib, and Ibn Zamraq, preserved their verses by having them inscribed in the Alhambra.

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