central asia the place where algebra was born

CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN? CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN? Sponsored by the following:       UNC Office for Diversity and Multicultural Affairs UNC Graduate School UNC Center for Slavic, Eurasian, and East European Studies Carolina Center for the Study of the Middle East and Muslim Civilizations UNC Cell and Developmental Biology Department Central Asian Focus Group CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN? CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN? CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN? CENTRAL ASIA: THE PLACE WHERE THE WEST AND EAST MET CENTRAL ASIA THE PLACE WHERE THE WEST AND EAST MET The Battle of Issus (333 BC) CENTRAL ASIA THE PLACE WHERE THE WEST AND EAST MET Hellenistic States, Greek influence till 2nd century AD CENTRAL ASIA: THE PLACE WHERE THE WEST AND EAST MET ZIAN QUANG,138-126 BC THE SILK ROUTE KHORAZM CALIPHATE       Prophet Muhammad, Arabia Abu Bakr - “khalifa” (>caliph) – (prophet’s) successor (632-634), Syria and Iraq, campaign against Sassanid Iran and Byzantium Omar (634-644), Iran and Palestine Uthman (644-656) immediate contact with Central Asia Ali (656-661) Umayyad caliphs (661-750), further expansion into Central Asia Expansion into Central Asia       Qutaiba ibn Muslim - 705-715 Romitan - 707 Varakhsha and Bukhara - 709 Shumon, Nasaf and Kesh - 710 Khorezm and Samarkand - 712 Shosh, Farghona and Koshghar - 715 CALIPHATE Practical Necessity to Develop Science      Finance, communication, calendar Trade relations, transportation, navigation Civil engineering, measurement of distances on the globe, direction to Mecca Levy tax, division of heritage justification of decisions Preservation and Development   Library devoted to translation and preservation Persian works, first from Pahlavi (Middle Persian), then from Syriac, Sanscrit, and Greek, under Caliph alMansour (754-775). Bait al-Hikma – House of Wisdom - was established under caliph al-Ma’mun (786833)- shift to research in mathematics, astronomy, philosophy... Algebra – Why?        Equations of various degrees and necessity to find solutions Babylon about 4000 years ago, by means of tables Egypt – Ahmes papyrus, about 2000-1700 BC Greece – geometric methods Diophantus – 3rd century CE, by means of tables India Maya, Aztec, Inca Breakthrough - Al-Khwārizmī  Born around 780, died around 850 Abū’Abd Allāh (Abū Ja’far) Muhammad ibn Musa alKhwārizmī alMajousi alKatarbali.  Al-Khwārizmī - Breakthrough  Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (820) (The Compendious Book on Calculation by Completion and Balancing) - algebra Kitāb al-jam wa-l-tafrīq bi-ḥisāb alhind (825)("The Book of Addition and Subtraction According to the Hindu Calculation") - arithmetic  Al-Khwārizmī - Books  Kitab surat al-ard ("Book on the appearance of the Earth" or "The image of the Earth"; (833), translated as Geography) Zīj al-sindhind ("astronomical tables") (820) Risāla fi istikhrāj ta’rīkh al-yahūd ("Extraction of the Jewish Era") Ma’rifat sa’at al-mashriq fī kull balad (on the morning width) Ma’rifat al-samt min qibal al-irtifā’ (the determination of the azimuth from a height)     Al-Khwārizmī - Books  Kitāb ar-Ruḵāma(t) (the book on sundials) Kitab al-Tarikh (the book of history) (the two have been lost)  Al-Khwārizmī - Books Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwārizmī Al-Khwārizmī - Algebra al-Kitab al-mukhtasar fi hisab al-jabr wa'lmuqabala (The Compendious Book on Calculation by Completion and Balancing) (820) al-jabr - “algebra” Geometric Method x2 + bx = c A1 A2 S2/4 A B B2 B1 x2 = S1 bx = S2 S2/4 S1 S2/4 x D1 D x S2/4 C C1 D2 C2 Geometric Method A2 B2 S2/4 B B1 S 1  x  surfaceABC D 2 A1 A b 4 x b 4 D1 S2/4 x S2/4 S2  4  x D D2 2 x S2/4 C C2 2 C1 b  b 2 x  bx  c  ( AA 2 B 2 BB 1C 1CC 2 D 2 DD 1 A1 )   x    4   2  4 or b b  x   c 2 4  2 2 b b  x   c 2 4  2 2  x b   c b   2 4  x b 2 x c b 2 2 2  c b 2 4  b 2 x b 2  c b 2 4 4 Al-Khwārizmī - Algebra 1) 5x2 = 40x 2) 25/5x2=100 3) 5x = 10 4) x2 + 10x = 39 5) x2 + 21 = 10x 6) 12x + 288 = x2 Al-Khwārizmī - Algebra 1) 2) 3) 4) 5) 6) squares equal roots squares equal number roots equal number squares and roots equal number squares and number equal roots roots and number equal squares Al-Khwārizmī - Algebra 1) 2) 3) 4) 5) 6) ax2 = bx ax2=c bx = c ax2 + bx = c ax2 + c = bx bx + c = ax2 Al-Khwārizmī - Algebra 1) 2) 3) 4) 5) 6) 1. 2. 3. 4. 5. 6. 5x2 = 40x 25/5x2=100 5x = 10 x2 + 10x = 39 x2 + 21 = 10x 12x + 288 = x2 squares equal roots squares equal number roots equal number squares and roots equal number squares and number equal roots squares and number equal roots ax2 = bx ax2=c bx = c ax2 + bx = c ax2 + c = bx bx + c = ax2 Al-Khwārizmī - Algebra 2x2 + 50 – 20x = 29 + x2 – 10x x2 - 10x + 21 = 0 ax2 + bx + c = 0 Al-Khwārizmī - Algebra  2x2 + 50 – 20x = 29 + x2 – 10x Aljabr - completion 2x2 + 50 + 10x = 29 + x2 + 20x Almuqabala - balancing x2 + 21 = 10x   Al-Khwārizmī Divide the number of roots by two Multiply it by itself Subtract number of it We b 2        b 2               2 b c 2                2 Extract square root of it b 2         2 c                 Subtract it from half number of roots x1  b  2 b 2 2 c or add it to half number of roots x1,2  b  2         b 2         2 c x1,2  b  2         b 2         2 c Al-Khwārizmī - Ariphmetic Al-Khwārizmī - Ariphmetic Al-Khwārizmī - Ariphmetic I, II, III, IV, V, VI, VII, VIII, IX, X, L, C, D, M CDLXXXVII - 487 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ABACI Al-Khwārizmī - Ariphmetic 487 x 15 487 x 15 2435 487 7305 4 2 0 4 8 3 0 7 1 5 5 7 3 0 5 Al-Khwārizmī Impact on European Mathematics  Al Kitab al muhtasar fi hisab aljabr va al muqabala • Robert of Chester, 1145 • Gerard of Cremona, 12th century • Leonardo of Pisa commented on 6 types of quadratic equations Al-Khwārizmī Impact on European Mathematics        Kitab al jam va tafriq bi hisab al hind - “Algorizm’s book on arithmetical practice” - Johannes of Toledo, 12th century. 1135 to 1153, The book spread in Europe. 13th c., Socrobosco, Algorismus Vulgaris (The Simple Algorism). Danish scholar Ingversen, comments in 1290. 13th c., Demonstratto de algorismo (The explanation of algorism) by Iordan Nomoraria. Besides, Algorithmus demonstatus (The explained algorism) is known. Nurnberg, 1534, and Paris, 1570. In Italian Tractatus algorismi (Treatise on Algorism), by Giacobo of Florence, 1307. Italian Prosdocimo de Beldomodo’s Algorismi tractatus peritulis et necessarus (The very useful and necessary treatise on algorism) Padua, 1483, Venice, 1540. 13th., poetic book Carmende algorismo (The song on algorism), French Alexander, in French, English, and Iceland. 14th century the French mathematician Nicol Orem’s Algorismus proportionus (The algorism of proportions). 15th century Peierbach’s book Algorithmus - the main aid book in the Austrian universities. Al-Khwārizmī Impact on European Mathematics        Kitab al jam va tafriq bi hisab al hind - “Algorizm’s book on arithmetical practice” - Johannes of Toledo, 12th century. 1135 to 1153, The book spread in Europe. 13th c., Socrobosco, Algorismus Vulgaris (The Simple Algorism). Danish scholar Ingversen, comments in 1290. 13th c., Demonstratto de algorismo (The explanation of algorism) by Iordan Nemoraria. Besides, Algorithmus demonstatus (The explained algorism) is known. Nurnberg, 1534, and Paris, 1570. In Italian Tractatus algorismi (Treatise on Algorism), by Giacobo of Florence, 1307. Italian Prosdocimo de Beldomodo’s Algorismi tractatus peritulis et necessarus (The very useful and necessary treatise on algorism) Padua, 1483, Venice, 1540. 13th., poetic book Carmende algorismo (The song on algorism), French Alexander, in French, English, and Iceland. 14th century the French mathematician Nicolas Orem’s Algorismus proportionus (The algorism of proportions). 15th century Peierbach’s book Algorithmus - the main aid book in the Austrian universities. Algebra after Al-Khwārizmī  In the East • Ghiyās od-Dīn Abul-Fatah Omār ibn Ibrāhīm Khayyām Nishābūrī or Omar Khayyam (1048 – 1131) • Ulugbek (1394-1449) • Ghiyāth al-Dīn Jamshīd ibn Mas’ūd alKāshī (c. 1380 – 1429) Algebra after Al-Khwārizmī  In the West • Niccolò Fontana Tartaglia (1499/1500 – 1557) cubic equations • Gerolamo Cardano (1501 - 1576) • Scipione del Ferro cubic equations • Lodovico Ferrari (1522 – 1565) • François Viète (or Vieta), (1540 - 1603), CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN Questions? Thank you