Worksheet Number Twelve Worksheet Number Fifteen. Amicable Numbers and thabit ibn qurra. We have seen thePythagorean concepts of perfect and amicable numbers earlier in this course. http://www.math.neu.edu/~gilmore/U201sp04files/201WS15.htm
Extractions: Worksheet Number Fifteen Amicable Numbers and Thabit ibn Qurra We have seen the Pythagorean concepts of perfect and amicable numbers earlier in this course. The last theorem in book IX of Euclid, Theorem IX.36 states that if is a prime number then is a perfect number. Examples are 6, 28, 496 and 8,128. This is the pinnacle of ancient Greek number theory. The only amicable numbers known to the ancient Greeks were 220 and 284. To find some formula similar to the one in Euclid, but for amicable numbers, must occur to some students of number theory. A successful such mathematician was Thabit ibn Qurra , who grew up in Harran, in what is now Turkey, and lived from about 836 to 901. He ended up being the court astronomer in Baghdad. ThabitÕs theorem giving a formula to construct infinitely many pairs of amicable numbers is the following: Theorem and have the property that are prime numbers. Then a = and are amicable numbers, with a an abundant number and b a deficient number. An abundant number has the sum of its proper divisors bigger than the number, like 12. A deficient number has thee sum of its divisors smaller than the number, like 9.
History Of Mathematics: Arabic Mathematics Habas alHasib (c. 850); thabit ibn qurra (836 -901); al-Fadl al-Nayrizi(c. 880); Abu Kamil ibn Aslam (c. 850-930); Qusta ibn Luka (d http://aleph0.clarku.edu/~djoyce/mathhist/arab.html
Extractions: Arabic Mathematics This page is under development. 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)
Untitled surds). Abu lHasan thabit ibn qurra Born 826 in Harran, Mesopotamia(now Turkey) Died 18 Feb 901 in Baghdad, (now in Iraq). thabit http://www.math.tamu.edu/~don.allen/history/arab/arab.html
Extractions: Arab Contributions Within a century of Muhammad's conquest of Mecca, Islamic armies conquered lands from northern Africa, southern Europe, through the Middle East and east up to India. Within a century of that the Caliphate split up into several parts. The eastern segment, under the Abbasid caliphs, became a center of growth, of luxury, and of peace. In 766 the caliph al-Mansur founded his capitol in Baghdad and the caliph Harun al-Rashid, established a library. The stage was set for his successor, Al-Ma'mum. In the 9 century Al-Ma'mum established Baghdad as the new center of wisdom and learning. He establihed a research institute, the Bayt al-Hikma (House of Wisdom), which would last more than 200 years. Al-Ma'mum was responsible for a large scale translation project of as many ancient works as could be found. Greek manuscripts were obtained through treaties. By the end of the century, the major works of the Greeks had been translated. In addition, they learned the mathematics of the Babylonnians and the Hindus. What follows is a brief introduction to a few of the more prominent Arab mathematicians, and a sample of their work
Sar-Sc: Positive Atheism's Big List Of Quotations a few glorious names without contemporary equivalents in the West Jabir ibn Haiyan,alKindi, al-Khwarizmi, al-Fargani, al-Razi, thabit ibn qurra, al-Battani http://www.positiveatheism.org/hist/quotes/quote-s1.htm
Extractions: Lyman Sargent Contemporary World Ideologies (1969), quoted from Laird Wilcox, ed., " The Degeneration of Belief " The history of American education would have been much different without New Harmony and other secular communities that emphasized education. Many of the people who joined these communities wanted to better educate themselves and their children, and they wanted to educate the outside world by their example. At the base of these communitarian ideals was a form of environmental determinism combined with the belief that people would choose to change to improve themselves, their children, and their environment. Members believed that intentional communities could provide a better life than could be achieved through private ownership and competition. Even with the high failure rate and the personal struggles involved, many communitarians continued to believe in cooperative lifestyles.
Pour La Science. -L infini en Chine. -thabit ibn qurra et l infini numérique. http://www.teleologie.org/OT/deboard/5128.html
Extractions: -L'infiniment petit en physique. [ C'est dans cet article à la page 119 qu'est dit : "On ignore encore pourquoi la nature semble apprécier le chiffre trois" et en est illustré son rôle particulier. Peut-être le french Doktor Sanchez a-t-il une réponse ? Sinon, il faudra attendre - quand même pas 20 ans ! - celle du sturm Doktor Weltfaust].
Tank You -L infini en Chine. -thabit ibn qurra et l infini numérique. http://www.teleologie.org/OT/deboard/5130.html
Extractions: Follow Ups Post Followup debord of directors FAQ Posted by e. K. on February 09, 2001 at 03:51:57 PM EST: In Reply to: Pour la science. posted by Dr. W on February 08, 2001 at 07:46:28 PM EST: : Il s'agit du numéro spécial de "Pour la science" [ édition française de "Scientific american" ] de décembre 2000. : -L'infiniment petit en physique. [ C'est dans cet article à la page 119 qu'est dit : "On ignore encore pourquoi la nature semble apprécier le chiffre trois" et en est illustré son rôle particulier. Peut-être le french Doktor Sanchez a-t-il une réponse ? Sinon, il faudra attendre - quand même pas 20 ans ! - celle du sturm Doktor Weltfaust].
Ummah.com Print_a Science Feature Muslim Scientists thabit ibn qurra (836 CE). thabit ibn qurra ibn Marwan alSabial-Harrani was born in the year 836 CE at Harran (present Turkey). http://www.ummah.com/science/printscfeature.php?scfid=13
SearchBug Directory: Science: Math: History: People AlSabi thabit ibn qurra al-Harrani - http//www-gap.dcs.st-and.ac.uk/~history/Mathematicians/thabit.htmlGives information on background and contributions to http://www.searchbug.com/directory.aspx/Science/Math/History/People/
Extractions: Nous remercions vivement M. Hourya Sinaceur qui nous a généreusement transmis son article sur l'infini mathématique paru dans le "Dictionnaire de Philosophie et d'Histoire des Sciences" et qui nous a accordé l'autorisation de le publier sur notre site. Infini mathématique La préhistoire Linfini offre peu de prise à l'expérience immédiate. Des myriades de brins d'herbe dans un pré, c'est un nombre très grand, mais pas infini. On trouverait une image plus suggestive dans les figures en abyme ou deux miroirs face à face. Mais même dans ces cas on poursuit en imagination un processus dont on ne perçoit effectivement que les premières étapes. L'infini cependant est présent dès qu'il y a mathématique. Les Grecs déjà l'avaient rencontré. Par exemple, Zénon dElée (V e siècle avant J. C) avec ses paradoxes sur la divisibilité à linfini dun segment de droite, les Pythagoriciens (VI e siècle avant J. C.) avec leur découverte de lincommensurabilité de la diagonale du carré, Eudoxe (début du IV e siècle avant J. C) dont la théorie des proportions permet de traiter de tels incommensurables (livre V dEuclide), Aristote (IV
Biography-center - Letter Q Eugene www.whonamedit.com/doctor.cfm/1105.html; qurra, thabit ibnwwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/thabit.html. http://www.biography-center.com/q.html
Extractions: 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 20 biographies Qalasadi, Abu'l al-
Uczony Heretyk - Nowinki Matematyczne - Wirtualny Wszech¶wiat Tabit ibn qurra (ok. 826901). Dokladna data urodzin Tabita ibn Qurry (Thabitibn qurra) nie jest znana; miesci sie w przedziale lat 824-836. http://www.wiw.pl/nowinki/matematyka/200102/20010219-001.asp
Extractions: W iw.pl Na bie¿±co: I nformacje C o nowego Matematyka i przyroda: A stronomia B iologia ... odelowanie rzeczywisto¶ci Humanistyka: F ilozofia H istoria ... ztuka Czytaj: B iblioteka D elta ... ielcy i wiêksi Przydatne: S ³owniki C o i gdzie studiowaæ ... szech¶wiat w obrazkach Jeste¶ tutaj: Wirtualny Wszech¶wiat Informacje Nowinki 2000-2002 Matematyka Jeste¶ tutaj nowinka: Tabit Ibn Qurra (ok. 826-901) Dok³adna data urodzin Tabita Ibn Qurry (Thabit ibn Qurra) nie jest znana; mie¶ci siê w przedziale lat 824-836. Wiadomo natomiast, ¿e Tabit pochodzi³ z Harranu w Górnej Mezopotamii (obecnie Turcja), gdzie podobno w m³odo¶ci para³ siê wymian± pieniêdzy. Miasto to by³o o¶rodkiem kultu astralnego: cz³onkowie tamtejszej sekty sabijczyków utrzymywali, ¿e jako pierwsi uprawiali ziemiê, budowali miasta i... rozwinêli naukê. Dzieje Harranu tak siê potoczy³y, ¿e jego mieszkañcy przyswoili sobie jêzyk grecki w epoce hellenistycznej, a po podboju przez Arabów - arabski, zachowuj±c jednak ojczysty aramejski wraz z religi± przodków. Niemniej wolnomy¶licielskie pogl±dy Tabita sprawi³y, ¿e popad³ w konflikt z sabijczykami i opu¶ci³ Harran. Wêdruj±c spotka³ na swej drodze matematyka Muhammada Ibn Musê Ibn Shakira (jednego ze s³ynnych trzech braci Banu Musa), na którym g³êbia wiedzy matematycznej i filozoficznej Ibn Qurry, jak równie¿ jego bieg³o¶æ w jêzykach wywar³y olbrzymie wra¿enie. Muhhamad zaprosi³ go do Bagdadu, gdzie pod rz±dami dynastii Abbasydów rozkwita³a nauka. Najwybitniejszym jej patronem by³ kalif Al-Mamun, który za³o¿y³ Dom M±dro¶ci (
History 935 B.C. philosophy. . Author References Ibrahim, ibn Sinan ibn Thabitibn qurra http//www.cwi.nl/~keesh/Iran/Maths/qurra.htm. Mac http://faculty.oxy.edu/jquinn/home/Math490/Timeline/935BC.html
Extractions: 935 B.C. At the age of twenty-seven, Ibrahim ibn Sinan, was the only known mathematician in the year 935 BC. He was born in the city of Baghdad in 908 BC, where he also died at the age of thirty-eight. Ibrahim ibn Sinans interests were in geometry, especially tangents to circles, astronomy, and mathematical philosophy. He also wrote several books on geometry, including On Drawing the Three Conic Sections , which explains the constructions of the ellipse, hyperbola, and parabola. By studying the geometry of the shadows of the sun, Sinan tried to describe what he thought was the motion of the sun. The most famous work of Ibrahim ibn Sinan was the quadrature of the parabola. From this problem, Sinan developed a method of integration that was more general than the previously defined technique by Archimedes. His book, On the Measurement of the Parabola , introduces a theorem that states that the area of a segment of a parabola is four-thirds times the area of the triangle inscribed in that parabola. Ibrahim ibn Sinan translated many Greek mathematical and philosophical works. Because of his work in mathematical philosophy, he has been labeled the "foremost Arab mathematician to treat mathematical philosophy." Author References:
The Mathematics Of Islam, Part 2 In this lecture, the topics consisted of alKhwarizmi (750-850), thabit ibnQurra (830-890), Abu-Sahl al-Kuhi (early 900s), ibn al-Haytham (965-1039 http://public.csusm.edu/public/DJBarskyWebs/330CollageOct01.html
Extractions: The presentation given today by Dr. Barsky generated an overall theme that the works of the mathematicians of Islam during the period of (965-1039) seemed to show traces of calculus, despite the fact that calculus came about later in time. In this lecture, the topics consisted of al-Khwarizmi (750-850), Thabit ibn Qurra (830-890), Abu-Sahl al-Kuhi (early 900s), ibn al-Haytham (965-1039), Mohammed's Flight from Mecca (622), the Battle of Tours (732), the period of Caliphates, the Fall of Baghdad to Seljuk Turks (1055), the beginning of the first Crusade (1096), the arrival of the Mongols under Ghengis Khan (early 1200s), al-Khwarizmi's truncated pyramid problem, Mishnat ha-Middot, and ibn al-Haytham's volume of a paraboloid calculations. We did not have a mathematician of the day, instead we talked about our papers that will be due October 8. We then covered more of the history of Islamic mathematics. We focused on al-Khwarizmi (750-850), Thabit ibn Qurra (830-890), Abu-Sahl al-Kuhi (early 900s), and ibn al-Haytham (965-1039). We concentrated on problems from al-Khwarizmi and ibn al-Haytham, which mainly dealt with finding volumes. I really enjoyed the lecture about the volume of a parabola from ibn al-Haytham. I have previously seen the symbol for (the sum of), but I usually stopped at that point because I did not understand, or I felt like it was too complicated. I understand the logic behind finding the circumscribed volume, and inscribed volume of the parabola. I can see that the difference between the two is the volume of the bottom disk of the circumscribed volume. I see that the (sum symbol) is included in equations that are interested in finding the sum of the differences between two estimates which will give you the solution to a problem. I also see that as you take the sum of the differences you are reaching the limit which is related to the volume of the parabola.
Teoremadepitagoras Translate this page La segunda escena se basa en la demostración que Meavilla (1989) atribuye a ThabitIbn qurra, matemático árabe del s.IX y se caracteriza por ser el puzzle http://www.cnice.mecd.es/eos/MaterialesEducativos/mem2002/geometria_triangulo/te
Extractions: Teorema de Pitágoras E n un triángulo rectángulo, la suma de los cuadrados de los catetos (b y c) es igual al cuadrado de la hipotenusa (a): a =b +c Los números a b y c que verifican esta relación se llaman ternas pitagóricas o números pitagóricos en alusión al estudio que de ellos hicieron Pitágoras y sus discípulos. Los antecedentes históricos de este teorema se remontan a las civilizaciones babilónica y egipcia en el segundo milenio a.J.C. El papiro Rhind y el de Moscú confirman la existencia de tablas de número pitagóricos en esa época. Tras las inundaciones del Nilo, los agrimensores egipcios construían triángulos rectángulos de catetos 3 y 4 y de hipotenusa 5, mediante una cuerda de 12 nudos para parcelar el terreno. Euclides demuestra el Teorema de Pitágoras en la proposición 47 del Libro I de los Elementos En los triángulos rectángulos el cuadrado sobre el ángulo opuesto al ángulo recto es equivalente a los cuadrados sobre los lados que forman el ángulo recto En la proposición 48 demuestra que si el cuadrado construido sobre uno de los lados de un triángulo es equivalente a los cuadrados, juntos, de los otros dos lados, el ángulo formado por esos dos lados es recto, es decir, el recíproco de la Proposición 47.
CONTENTS The summary for this Arabic page contains characters that cannot be correctly displayed in this language/character set. http://www.ias-worldwide.org/contents_noble.htm
Extractions: Academy Publishes " Personalities Noble" CONTENTS Abu Abdullah al-Battani Abu Raihan al-Biruni Abu Wafa Muhammad al-Buzjani Abu al-Naser al-Farabi Al-Farghani Abu Hamid al- Ghazali Al- Idrissi Ibn al-Bitar Abu Ali Hassan Ibn al-Haitham Ibn Al-Nafis Ibn Khaldun Ibn Rushd Ibn Sina Abu Marwan Ibn Zuhr Jabir Ibn Haiyan Mohammad Bin Musa al-Khawarizmi Omer al-Khayyam Yaqub Ibn Ishaq al-Kindi Abu al-Hassan Ali al-Mas'udi Abu al-Hassan al-Mawardi Mohammad Ibn Zakariya al- Razi Jalal Al- Din Rumi Ali Ibn Rabban al-Tabari Thabit Ibn Qurra Nasir al-Din al- Tusi Abu al-Qasim al-Zahrawi
Extractions: Ibazizen Augustin Ibn Abd Al Wahhad Ibn Abi Taleb Imam Ali Ibn Abi Zayd Al-Qayrawani La Risala (dogme de l'islam selon le rite malekite-bilingue) Ibn Abi Zayd Al-Qayrawani La Risala (dogme de l'islam selon le rite malekite-bilingue) Ibn Al Baytar,trad.Lecler Ibn Al Farid (Omar) La grande Taiyya : la voie mystique Ibn Al Faridh Omar L'Eloge du vin (trad.Dermenghem) Ibn Al Zayyat al Tadili Regards sur le temps des Soufis:Sud marocain V-VI-VIIs.Hegir Ibn al-Jawzi Ibn Al-Muqaffa Abdallah Le livre de Kalila et Dimna Ibn Al-Muqaffa Abdallah Le pouvoir et les intellectuels:aventures de Kalila et Dimna Ibn Arabi La profession de foi Ibn Arabi L'Alchimie du bonheur parfait Ibn Arabi Ibn Arabi L'Arbre du monde Ibn Arabi Le livre de l'arbre et des quatre oiseaux Ibn Arabi Les Soufis d'Andalousie Ibn Arabi Ibn Arabi Ibn Arabi Le livre d'enseignement par les formules indicatives... Ibn Arabi Le Livre de l'extinction dans la contemplation Ibn Arabi Ibn Arabi Les Illuminations de la Mecque Ibn Arabi Ibn Arabi La parure des Abdal Ibn Arabi Ibn Arabi Ibn Arabi Le voyage spirituel Ibn Arabi Les Soufis d'Andalousie,la vie merveilleuse de Dhu-l-Nun
Ursula Weisser Epitome of Galen s Book on Seven-Month Children Edition.Journal for the History of Arabic Science 7 (1983) S.141-150. http://www.rrz.uni-hamburg.de/Mittelalterforschung/WeisserText.htm
Extractions: Adresse Prof. Dr. Ursula Weisser Institut für Geschichte der Medizin Universitäts-Krankenhaus Eppendorf Martinistr.52, 20246 Hamburg Geschichte der Medizin F orschungsschwerpunkte Medizin im arabisch-islamischen Mittelalter Die wissenschaftliche Medizin im Islam baut fast vollständig auf den Kenntnissen und Vorstellungen der Antike auf. Daher liegt bei den folgenden Projekten das Hauptgewicht auf der Frage, in welcher Weise dieses antike Erbe aufgenommen, weiterverarbeitet und modifiziert wurde. Da wesentliche Inhalte der antiken Medizin dem Abendland zunächst vorwiegend durch Übersetzungen arabischer Werke vermittelt wurde, wird auch die Nachwirkung solcher Modifikationen im lateinischen Mittelalter berücksichtigt. 1. Zeugungslehren in der arabisch-islamischen Medizin Erschließung von (kleineren) arabischen Texten durch Edition und Übersetzung. - Untersuchungen zu den Vorstellungen der islamischen Ärzte insbesondere in ihrem Verhältnis zu denen ihrer antiken Autoritäten. Dieses Teilgebiet der Physiologie bietet ein Musterbeispiel für die überwiegend literarisch-spekulative Behandlung humanbiologischer Fragestellungen im islamischen Mittelalter. Veröffentlichungen: Die hippokratische Lehre von den Siebenmonatskindern bei Galen und Tabit ibn Qurra. Sudhoffs Archiv 63 (1979) S.209-238.