The Rise of Islamic Mathematics 8 th – 13 th Century

622 A.D. Mohammed escapes from Mecca to Medina The day he arrives at Yathrib El Medinat (Medina) is the beginning of the new year in the Islamic Calendar Returned to Mecca a hero and unites the scattered tribes

Arab-Islamic Expansion India Persia Mesopotamia Northern Africa Spain

Arab-Islamic Expansion Caliph – An Islamic leader acting in Mohammed’s place after his death in 632 AD Eastern Caliph – reigned in Baghdad Western Caliph – reigned in Cordoba

Preservation of Culture of Conquered Territories Arabs seized upon Greek and Hindu Erudition Invited distinguished scholars to their courts Translated Hindu and Greek works in Astronomy Medicine Mathematics Saved until Europe scholars came out of Dark Ages “Cubic Equations and Intersections of Conic Sections” by Diophantus translated to Arabic kept in Tehran University

The House of Wisdom Established by caliph al - Rashid Primarily a Library When his son had a dream of Aristotle, he made translating Greeks texts his goal Place for Translation and Research Scholars would work here in translating Greek and Hindu treatises to Arabic

766 AD caliph al-Mans ûr Brahmagupta’s works brought to Baghdad Hindu Numerals brought into Arabic mathematics 786 AD caliph Harun al- Rashid Euclid’s Elements translated 809 AD caliph al M âmûn An observatory was built Measured Earth’s meridian Translated mathematical and astronomical work Almagest

Thabit Ibn Qurra: AD Physician, Philosopher, Linguist, Mathematician Best Translations Ptolemy Appollonius Archimedes Theodosius Euclid

Abu’l Wefa: 940 – 998 AD Born in Persian Mountain Region of Khorasan Translated Diophanthus Father of Algebra First solution of Cubic Equations Found Rational Solutions to Curves Perfected Ptolemy’s method of computing sine to nine decimal places

10 th and 11 th Century and before 7 th century: Arabians wrote all numbers in words Extensive Conquering: Introduction of short symbolism Ciphered System (like Ionic Greek) Adopted Hindu Notation adopted by merchants Hindu numerals excluded in Eastern Empire Arabic Numeral System

Al-Khowarizimi: AD Rules for Computing Modeled after Hindu Algorithms Casting out 9’s False Position Double False Position Rule of Three CASTING OUT NINE’S

Al-Khowarizimi Popularized number zero Algebra Used geometry to prove algebraic results Worked in astronomy

Al-Khowarizimi Wrote a treatise on Hindu-Arabic numerals Introduced number zero Introduced Hindu concept of decimal positioning

Al-Khowarizimi Wrote treatise entitled Kitab al-jabr wa’l-muqabalah Practical application of algebra to Islamic Inheritance Laws Al-jabr means “restoration” or “completion” Al-muqabalah means “balancing”

Completing the Square

Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

Geometry in Art

Abu Nasr al-Farabi: AD

Alhambra of Granada, Spain

Alhambra Symmetrical Patterns