Spanish mathematicians


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Trabajo realizado sobre los matemáticos y pensadores andalusíes para un proyecto eTwinning.

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Spanish mathematicians

  1. 1. Spanish mathematicians in Al- Andalus Performed by students of 2nd ESO IES Odra-Pisuerga for proyecto eTwinning "Sharing Geometry"
  2. 2. In Europe, mathematics has no origin as old as in many countries in the Far and Middle East, reaching only notable successes in the medieval era and especially developed in the Renaissance. In the Middle Ages can be seen certain cultural obscurantism, no doubt because of war and social events of the time. Only some religious monasteries some manuscripts, evidence of a cultural awakening first were written. Mathematics comes to Europe from contact with the Arabs. Until that time, the geometry of the Greeks to which he had not been added almost nothing was known. It was the Arabs who introduced the decimal system, and zero positional Hindus and generalized by the Arabs, Algebra and Trigonometry in the countries they conquered numbering. The numbers were natural, rational, irrational, all positive. The negatives were false solutions. After reading the book "The Lord Zero" have made this little research on the role of the Arabs in Spain in the development of mathematics during the Middle Ages.
  3. 3. - Expansion in the time of Muhammad years 622 – 632 - Expansion during the Orthodox Caliphate years 632-661 - Expansion during the Umayyad Caliphate years 661-750 Fuente: Wikipedia Map of the Arab expansion from Muhammad to reach the Al-Andalus
  4. 4. The birth of Arab figures In the ninth century to the unity of the Arab-Muslim empire have disintegrated and North Africa and Muslim Spain no longer belonged to the Caliphate of Baghdad, but due to pilgrimages to Mecca, were frequent commercial exchanges. When East Arab met Hindu arithmetic, quickly spread throughout the Maghreb and Spain. Until then, Western calculators used archaic methods, but from the mid-ninth century Hindu figures also used as their eastern brethren, and, like them, the writing in the sand. At first, the script was very similar, but has evolved over time, and it is these Western Arabic numerals, also called "ghobar figures" which, from Spain, becoming the Christian peoples of medieval Europe.
  5. 5. Around the year 967, a French monk named Gerbert d'Aurillac, traveled to the court of the Count of Barcelona, ​​Borrell II, where he remained three years in the monastery of Santa Maria de Ripoll, Gerona, where possibly traveled to Cordoba and Sevilla, which allowed him to make contact with Arabic numerals and started the study of mathematics and astronomy. Then he taught at Reims where he taught and spread the Arabic numerals. He later became Pope with the name of Sylvester II. By Celia Ruiz García In addition to spreading the Arabic numerals, popularized the use of the astrolabe is an astronomical unit. He also produced a new version of the monochord, a consistent musical instrument in a soundboard on which a variable-length string with which the sound vibrations were measured and tense musical intervals Gerberto d’Aurillac, the mathematician Pope
  6. 6. The Toledo School of Translators In the cultural environment of the mid-twelfth century born a phenomenon known as the School of Translators of Toledo, which was not a school but a group of Christian, Jewish and Arab scholars who worked together in research and translation of all Arab culture works of antiquity. It was a way to make them known to the rest of Europe. By Diego Merino Martínez This was during the first period with Archbishop Raimundo. During a second period with Alfonso X the Wise, specially treated for Astronomy, Physics and Mathematics translated. Thanks to this great boost Monarch Azarquiel treaties, Ptolemy and Abu Ali al-Haitam, but also works as recreational chess books, craps tables and collections of short stories as fruitful for Western literatures as Kalila and Dimna resulted and Sendebar. In this second phase translations are no longer done in Latin but in Castilian. Original works as the astronomical tables of Alfonso was also composed.
  7. 7. Abu-l-Qasim Maslama called al Mayrity Abu Al-Qasim Maslama born in Madrid in the mid- tenth century and died in Córdoba in 1007. Was very young I traveled to Córdoba where he was a pupil of important mathematicians as' Muhammad ibn Abd al Gafir and astronomer Abu Bakr ibn Abi Isa. He was an important scientific school in Cordoba where they studied and important mathematical astronomers as Ibn al Samh, Ibn al-Jayyât, Ibn al- Saffar, al-Zahrawi , Ibn-Khaldun and Kirmani. He wrote several works of commercial arithmetic, but more important is a Commentary on Ptolemy's Planisphere. He also wrote a short treatise on the astrolabe where its technical construction and instructions on their use is described. Both his works as his disciples enjoyed great fame and popularity throughout the Arab world and Latin of his day, and also had a decisive importance as a basis for the construction of the spherical astrolabe conducted later astronomers court of King Alfonso X the Wise. By J. Manuel Martín García
  8. 8. Summary table of the main disciples of Abu al-Qasim Maslama Abulhasar Ali Abensuleiman al-Zaharwi Born in Medina al-Zahra, near Cordoba city. He was wise in arithmetic and geometry. He practiced medicine with a big fame. He wrote about commercial contracts. He lived in Seville where he prospered as a wise illustrious. Abulcasim Asbag Abenmohámed el Garnati ibn al-Samh Born in Granada about 980 and died in the same city in 1035. Mathematical genius, knew of Arithmetic, Geometry and Astronomy. He also delved into grammar and Medicine. Alfonso X studied astronomy books and is believed to have written the manuscript could Arithmetic deposited in El Escorial, short treatise on arithmetic and computer to teach the simplest figures and calculations. Abuabdallah Muhammed Ibn Saffar al Cortobi Born in Córdoba of a noble family with scientific tradition. He became a scholar in Literature and Calculus. Became blind and paralyzed but this did not prevent him from devoting himself to teaching. He made a brief treatise on the astrolabe. After traveling in Morocco, Fez, Tunis and Baghdad, he returned to Spain where he died
  9. 9. Abubequer Ibn al Jayyat. Born in 980 got great command of mathematics and astronomy, especially in Geometry and Arithmetic. He was court astrologer of Cordoba, Toledo and Zaragoza. Abumoslem Omar Banahmed Ibn Jaldun al Jadram Born into a distinguished family in Seville, was educated in Córdoba. He died in Seville in 1057 after having achieved fame as a philosopher, mathematician, astronomer and physician. The remarkable influence of Maslama also evident through the huge number of his works which were translated into other languages ​​such as that performed in the twelfth century Johannes Hispalensis of the work to that entitled al-Muamalat o “Liber Mahameleth”. This book has a theoretical part where is the theory of proportions and arithmetic operations and procedures which give good approximations for square roots inaccurate. References on solving equations of first and second degree are also given. They end up leaving Córdoba and leave to other cities where each was creating school so that several generations of mathematicians succeeded fairly competent around Al- Andalus.
  10. 10. Abu l-Hakam Amr ibn Abd al-Rahman ibn Ahmad ibn Ali al-Kirmani Born in Córdoba, where he was a pupil of Maslama, and died in Zaragoza in 1066. He was a mathematician, philosopher and physician who transmitted important knowledge of Eastern culture in Al-Andalus after traveling to major cities in the Arab East to study mathematics, medicine and astronomy. Throughout these trips not only acquired these traditional scientific knowledge, but also philosophical and literary, being the introducer of The Encyclopedia of the Brothers of Purity, Neoplatonic movement. A little later he moved to Zaragoza serving three kings of Taifa of Zaragoza in the second half of the eleventh century, Al-Muqtadir, Al-Mutaman and Al- Musta'in II, which was the grand vizier. Thus arose several scientific foci, in which mathematics was just a science practiced by scholars versed in multiple disciplines. By Jorge Pérez Nogales
  11. 11. Ibn Mu'adh al-Jayyani By Andrea Ortega We know he was born in Jaén, although the exact date is unknown. Member of a prominent family jienense Muslim jurists . Some of his ancestors were Kadis of Jaén, Córdoba and Seville . He himself was qadi of Jaén and Sevilla vizier . He traveled to Egypt during his trip to Mecca , where he came into contact with mathematicians of the time in the East. His fundamental contributions to mathematical knowledge were making mathematics understandable ratio of incommensurable magnitudes contained in the fifth book of Euclid's Elements as a rational reason ; make the first work or treatise known spherical trigonometry, largely thanks to the contributions of Egyptian mathematicians , which resolved several theorems and all problems arising in the spherical triangles when four of its elements are known and also , collected in a systematic way the mathematical knowledge of the time . Abd'Allah Muhammad Ibrahim al-Yayyani was a mathematician Al-Andalus, which particularly noted for his research and contributions in trigonometry, which was first dissociated studies astronomyi.
  12. 12. Al-Mutamán, the geometer King Yusuf Al- Mutamán was king of the Taifa of Zaragoza between 1081 and 1085 . He was a scholar king, protector of science and mathematics scholar The masterpiece in the intellectual field of Al- Mu'tamán was his Book of perfection and optical appearances Kitab al- Istikmal besides being a compendium of Greek mathematics of Euclid and Archimedes among others, and transmit Thabit ibn Qurraa teachings, the Banu Musa and Ibn al- Haytha enter original theorems. His work was transmitted through Maimonides to Egypt, and from there spread throughout central Asia, documenting even in Baghdad in the fourteenth century, but its influence did not reach the West. It studies the irrational numbers , conic sections , squaring the parabolic segment , areas and volumes of various geometric shapes or drawing of the tangent of a circle , among other mathematical problems. A Al-Mutamán se debe la primera formulación conocida del Teorema de Giovanni Ceva, que no sería conocido en Europa hasta 1678 By Óscar Porro Teorema de Ceva
  13. 13. Aben Essamej Mathematical hispano-arabic, S. XI, also a disciple of Abu Al-Qasim Maslama. Among his works are the 'Comments treaties Euclidean Geometry', as an introduction to mathematics. 'From the nature of numbers', 'From the calculations used in commerce' as well as a Master of Mathematics treaty, very remarkable work in those days. 'Treaty on the construction and use of the astrolabe', in collaboration with his disciple Aben Essofar. Astrolabe Essamej also wrote astronomical Tables and a Treaty of Mathematics. The astrolabe is possibly the oldest computer pocket officially known. This mechanism was used to determine the position of the heavenly bodies, or had a way to capture in his wit, all sky map of the time were, with only placed by a technique of angular position astrolabe itself. By Luis Miguel González
  14. 14. Abu Muhammad Jabir ibn Aflah Arab mathematician and astronomer whose Islah al-majisti (Correction of the Almagest) proved to be a strong influence on scholars throughout the Mediterranean and Europe. As native of Seville, Aflah knew Moses ben Maimon (Maimonides, 1135-1204). He developed a theorem in spherical trigonometry that bears his name, and created an instrument called the Torquentum for making transformations between spherical coordinates. His critique of Ptolemy's (c. 100-170) Almagest exerted an impact on a number of thinkers, among them Ibn Rushd (Averroës, 1126-1198). Born in Seville in 1100 and died in 1150. Gerolamo Cardano noticed that much material on Regiomontanus spherical trigonometry was plagiarized the work of the twelfth century Jabir ibn Aflah By Antonio González The Torquetum
  15. 15. Abraham Bar Hiyya He was a mathematician, astronomer and philosopher Hebrew . Born in Egypt in 1065, he lived in Barcelona and scientifically trained in the Courts of Zaragoza where he held various positions including Chief of the guard earning him the nickname Savasorda . Developed several scientific abstracts in Hebrew, from Arabic sources, and translated numerous Arabic and Hebrew into Latin works. Among his major works include Foundations of intelligence and belief tower. The shape of the earth, which is the first treatise in Hebrew on astronomical geography, as well as Book of computing the calendar. It is one of those who were responsible for transmitting to Europe 's great Jewish Andalusian Arabic science and , in particular , of the Upper and Zaragoza . For example , the quadratic equation and its solution have a very ancient origin and were known as algorithms to solve it in Babylon and Egypt. In Greece was developed by mathematician Diafonto Alexandria. So their solution was introduced to Europe by the mathematician Abraham bar Hiyya . By Ricardo Manrique Esteban
  16. 16. Abraham Ben Ezra By Julia García He was born in Tudela (Taifa of Zaragoza) in 1092 and died in Calahorra (Kingdom of Castile) in 1167. He was one of the most distinguished Jewish men of letters and writers of the Middle Ages. Ibn Ezra excelled in philosophy, astronomy/astrology, mathematics, poet ry, linguistics, and exegesis; he was called The Wise, The Great and The Admirable Doctor. Its importance is due to the Arab mathematical spread across Europe. One of his most important works dealing with the description of the decimal place for values ​​of the numbers vary depending on their position from left to right. Also dealt with the zero and also translated the commentary of Al- Biruni on the boards of Al-Khwarizmi on the introduction of the current Indian figures in Arab mathematics. Ezra Calendar
  17. 17. Azarquiel, the Andalusian astronomer Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī was born in Toledo in 1029 and died in Seville in 1087. From humble beginnings, he worked as a blacksmith, which led to the construction of scientific precision instruments, as astrolabes, at the request of Arab and Jewish astronomers. Communication with these scholars and intelligence of Al-Zarqali could lead to a remarkable understanding of astronomical science self- taught, which led him to create innovations from astrolabe, as azafea. His work mainly known through the translations made ​​in astronomy specialists responsible for the actual scientific work scriptorium of Alfonso X the Wise. Thus, between 1225 and 1231 also Toledo Jewish Yehuda ben Moshe and Guillelmus Anglicus translated his Treatise on azafea into Latin, which was poured in the years 1260 to Castilian by the Toledo same Jew named in the prologues of alfonsíes works Yehuda Fly Fly or the Coheneso. By Alejandro Merino
  18. 18. Al-Qalasadi Abu al-Hasan Ali bin Mohammed bin Ali al-Qurashi al-Basti (Baza, Granada, 1412 - Beja, Tunisia Current, 1486), was one of the most important mathematical granadís. He studied philosophy, mathematics and science partition inheritance, very important in the Arab tradition. Pilgrimage to Mecca and he could always housed in a cultural environment madrasas where they lived. He had many disciples and wrote several works among which 12 Algebra, including: -Treatise on Arithmetic and Algebra, translated into several European languages ​​and was a major advance in the mathematics of his time. With it contributed to algebraic symbolism using the Arabic alphabet characters as mathematical symbols, expressing the equations with letters and short words that have symbolic value. - Classification of Arithmetic Science, which was very popular in North Africa . Finally al- Qalasadi used in both the arithmetic treated as in his writings on succession partitions identical to modern symbolism to represent the fraction , the numerator over the denominator meeting both separated by a horizontal line. By Roberto de la Orden
  19. 19. This is our small contribution to the knowledge of the great mathematicians and thinkers that existed in Al-Andalus, in an age when the study and development of science in Europe was stagnant On the other hand, keep in mind that in Arab schools or madrasas, not only studied math. Teachers and students were true humanists, knowing all sciences, so we speak of mathematicians who were doctors, philosophers and especially astronomers. Keep in mind that for the Arab knowledge of the daylight hours were very important to their prayers. Other great humanist thinkers not as dedicated to mathematics were Averroes, Maimónides and Said Al-andalusi.
  20. 20. Averroes Abū l-Walīd Muhammad ibn Ahmad ibn Muhammad ibn Rushd born in Cordoba on April 14, 1126 and died in Marrakech on December 10, 1198. It was an Andalusian philosopher and physician, a master of philosophy and Islamic law, mathematics, astronomy and medicine. The Cordovan philosopher thinks differently Aristotle to emphasize the role of sensory nerves in the brain and recognize the location of some intellectual faculties as imagination or memory. Averroes places the origin of the human intellect in sensory perception of individual objects and concrete end in globalization. He tried to clarify how human beings think and how the formulation of universal and eternal truths from perishable beings is possible. It was an important philosopher of thought By Arturo Padilla
  21. 21. Maimónides By Martín Angulo Moshé ben Maimón o Musa ibn Maymun also called from the Renaissance Maimonides was a physician, rabbi and Jewish theologian of Al-Andalus in the Middle Ages. Was important philosopher in medieval thought. Born in Córdoba (Spain), on March 30, 1138, in the midst of a distinguished family, paternally, of rabbinical judges, scholars and community leaders, documented from the tenth century. It started small and their biblical and Talmudic studies in the city of Córdoba , but in 1148 a wave of Almohad fanaticism caused his family had to pretend his conversion to Islam and change of residence often Al- Andalus. He lived in the city of Almeria , where he gave shelter in his house to his master Averroes , until moving in 1160 with her children to Fez. There he lived for only five years, because of the Almohad intolerance that forced them into exile , first for a few months in Palestine and finally Egypt. Maimonides lived there the rest of his life with his family in the city of Alexandria and later in Fustat (now Cairo , Egypt ), where he earned a living to practice medicine in the court of the Vizier Saladin, and then in the vizier al- Fadl , eldest son of Saladin. The Guide for the Perplexed ( 1190 ) , poorly dubbed Guide the wayward , is the key to his philosophical thought and exerted a strong influence on both Jewish and Christian circles especially scholastics.
  22. 22. Said al-Andalusi Abu- l -Qa'im ibn Said, called Said al- Andalusi (Almería, 1029 - Toledo, July 6, 1070 ) was a scientist, historian of philosophy and science and Hispano- Muslim jurist . The diagnosis was scientist in mathematics and astronomy. contributed in Toledanas Tables and, with Azarquiel he perfected with more accurate estimates of access and movement recess of the fixed stars , contrary to the Ptolemaic theory. The only work of Said al- Andalusi that remains is Kitab al- Tabaqat uman (Book of the categories of nations ), where he studied the universal development of philosophy and science. He wrote in Toledo in 1068 , when the author was 39 years old . It demonstrates objectivity, impartiality and critical approach to the subject . According to him there are only eight "nations" with scientific contributions : Indians , Persians, Babylonians , Greeks , Byzantines, Egyptians, Israelis and Arabs. Among these stands the Andalusian . It focuses on mathematics , astronomy , medicine and human geography , and other fields of study. It was used as a source for many other stories of science in medieval and modern times. By Martin Escalona As historian of science is an essential tool for the study of ancient and medieval science source and science in Al- Andalus.
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