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AL-Khwarizmi in the house of wisdom Founder of Algebra

AL-Khwarizmi in the house of wisdom Founder of Algebra. PH Ludwigsburg University of Education. By: Elham Vaseghi elham.vaseghi02@stud.ph-ludwigsburg.de January 2019. Persian mathematician. Muhammad ibn Musa Al- Khwarazmi

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AL-Khwarizmi in the house of wisdom Founder of Algebra

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  1. AL-Khwarizmi in the house of wisdomFounder of Algebra PH Ludwigsburg University of Education By: ElhamVaseghi elham.vaseghi02@stud.ph-ludwigsburg.de January 2019

  2. Persian mathematician Muhammad ibn Musa Al-Khwarazmi ( Abu Jafar/Abu Abdallah Muhammad ibn Musa Al-Khwarizmi) • Born around 780 AD • Place of birth : Khwarazm in old Persia (Modern Khiva) • Abbasid Dynasty (Islamic golden age) • Died around 850 AD

  3. Map of THE abbasiddynasty Kharazm • Marv Persian Gulf

  4. House of wisdom • Established in the early 9thcentury • A library and a place for: • Translation of books on mathematics, medicine, philosophy, logic, geography, astronomy, alchemy • from Greek, Hindu, Sanskrit, Persian, Chinese and Hebrew to Arabic • Centre of learning • Culmination point during the caliphate of Al-Ma’ mun Hause of wisdom(Bayt al-Hikma)

  5. Hause of wisdom • Developedintotheworldlargestrepository of books • Scholars from all over the Islamic Empire cametostudy and teach • Golden age of islamic civilization • Al Khwarizmi head of house of wisdom, around 820 AD • Destroyedby the Mongols (1258)

  6. Contributions • Geography • Astronomy • Cartography • Mathematics - Algebra - Arithmetic - Trigonometry • Hebrew calendar, “Extraction of the Jewish Era” • And some other works A stamp issued September 6, 1983 in the Soviet Union

  7. Developing SUNDIAL AND ASTORLAB Developed sundial to determine time of day from position of the sun in the sky (especially for time of prayer) Book :KitabAl-Rukhamat (lost) He also wrote two books on using and constructing astrolabes (lost) using and constructing astrolabes

  8. Astronomy • Two equipped observatories were constructed • Knowledge of astronomy was critical for Muslim exercises such as: - Determining direction pray - Setting of the crescent moon • Most of al-Khwarizmi’s contributions were in astronomy Book: Zij al-Sindhind ) lost) Astronomical Tablescontain calenders, calculations of the positions of the sun, moon and five planets known at his time Determined the direction ofMecca

  9. Geography • Book: Image of the earth • Provided the latitudes and longitudes of 2,402 cities and landmarks • Corrected and improved Ptolemy's data The World Map of al-Ma′mun

  10. Trigonometry • Accurate sine and cosine Tables Called them Jaib and inverse Jaib Jiva (Sanskrit) meanshypotenuse Mistake of Latin translator Jeib: Bay Sinus • First Table of Tangents • He was also a pioneer in spherical trigonometry

  11. Arithmetic • Ḥisābal-Hind • Book: Hindu Calculation • The original book lost • AccurateLatin translation dose not exist • (only some interpretations exist) • The English word “Algorithm" stems from “Algorizmi” • Algorithm means how to find the solution for a given problemo • theLatin form of al-Khwarizmi's name Page from a Latin translation, beginning with "Dixit Algorizmi"

  12. Arithmetic • Introduced the Hindu-Arabic numbers Disseminated the Indian numbers throughout the Islamic world and introduced them as “Arabic” numerals to the West.  He developed the decimal system and operations on fractions • Adapted the idea that zero is a number and explained the use of Zero Zero comes from the Arabic “Sifr” English : cifra , cipher German : Ziffer French : chiffre Latin translation of his work introduced the decimal system to the western world

  13. Algebra • First book on mathematic: • “al-jabrwal-muqabala“ • (Completion and balancing) • or • “al-Kitabal-mukhtaṣarfi ḥisabal-jabrwal-muqabala” • (The Compendious Book on Calculation by Completion and Balancing) • About100 pages A unique Arabic copy is kept at Oxford A Latin translation (1831)is kept in Cambridge

  14. al-jabrwal-muqabalacompletion and balancing Book content: • Abstract Divided writers in three groups • Purpose Introducing a kind of arithmetic for solving real life problems like: I. Dealing with each other II. Measuring the land III. Dividing inheritances • Reference - Theory -Applied

  15. al-jabrwal-muqabalacompletion and balancing • Theory 1. Theory of equations 1.1. Definition of vocabulary(notation) Shay : UnknownVariable/ Root Spanish wrote xay (“x” Pronounce “sh”) In time this word was abbreviated as x Mal : Square of unknown Derham : the amount that is known constant

  16. al-jabrwal-muqabalacompletion and balancing 1.2. Classifying the equations 1.3. finding the algorithm of each equations squares equal roots (ax2 = bx) squares equal number (ax2 = c) roots equal number (bx = c) squares and roots equal number (ax2 + bx = c) squares and number equal roots (ax2 + c = bx) roots and number equal squares (bx + c = ax2)

  17. al-jabrwal-muqabalacompletion and balancing 1.4. Defining two operations 1.4.1. Al-gabr Means completion or restoration. The process of removing negativeterms from an equation. Example: The equation x2 = 40 x - 4 x2 transforms into 5 x2 = 40 x “Algebra" comes from the Latin form of “Algabr”

  18. al-jabrwal-muqabalacompletion and balancing 1.4.2. Al-muqabala Means balancing Process of reducing positive terms of the same power when they occur on both sides of an equation. Example: Two applications of "al-muqabala" reduces 50 + 3x + x2 = 29 + 10 x to 21 + x2 = 7 x 1.5. Geometric justification By drawing figures he explained that his algorithms are correct and provable

  19. al-jabrwal-muqabalacompletion and balancing 2. Arithmetic of binomial expressions: Defining operations (+,-,*) on binomial terms RoshdyRased Mathematician and historian of science Beginning of the process of “Arithmatisationof Algebra”

  20. al-gebra before kharazmi • Babylonia Earliest civilization recorded to have solved quadratic problems. • Diophantus • Brahmagupta • Salomon Gandz (1925), algebra and book of Mishnat ha- middot 2000 1000 0 1000 2000

  21. Founder of Algebra Characteristics of Al-khawrizmi’s works: • Algebra as an independent discipline. Presenting the first systematic solution of linear and quadratic equations. • Innovatemathematical vocabularies that could be easily extended. Mathematic Language • Disarranging former Greek math classifications. Used to categorize Arithmetic and Geometry as science of discrete and continuous quantities, respectively.

  22. Impacts on others • AbūKāmil, Shujāʿ ibn Aslam • Abu bakr Karaji • Omar Khayam 1. Geometric solutions of cubic equations. 2.Calculating the accurate length of a year (365 days, 5 hours and 49 minutes). Note: The solar Hijri calendar was developed accordingly that has only 24 hours deviation within each 4 Million years. (Gregorian calendar has 24 hours deviation within each 2000 years) • Leonardo daPisa ( Fibonacci) Omar Khayam Leonardo Fibonacci

  23. conjecture • The earth might be spherical • There might be a land in western point of the Earth. Christopher Columbus explored about 8 century later. In recognition of his services to the scientific world NASA has named a crater on the moon for him

  24. Thank you for your attention

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