100%(2)2 out of 2 people found this document helpful
This preview shows page 29 - 32 out of 37 pages.
Serious mathematical sciences were learnt by the Arabs from the Greeks. [but not everything was learnt from them]Two main sources of the early information of the theory of numbers [not Arab]1)Elements by Euclid: 1stmajor Greek mathematics book - translated by Ishaq bin Hunayn [later revised by Thabit bin Qurrah– translator of most mathematical works]
2)The Introduction to the Science of Numbers by Nicomachus: translated by Thabit bin Qurrah. This book strongly influenced the authors of the Epistles ofthe Brethren of Sincerity.For the ancient Greeks [Elements], irrational numbers existed as geometrical magnitude. However, some Islamic mathematicians prefer to express ratios in terms of continued fractions but eventually regarded all ratios as numbers.Thabit bin Qurrah:Wrote noteworthy remarks on infinite collections, believing that an infinite collection could be a part of another infinite collection. Was one of the mathematicians that worked on parallel problems. He argued that motion is at the base of the whole of geometry. [supportedby Ibn al-Haytham, refuted by al-Khayyami].Umar al-Khayyam:Persian polymath.Philosopher, mathematician, astronomer and poet.Wrote treatises on mechanics, geography, mineralogy, music and Islamic theology.Wrote the influential Treatise on Demonstration of Problems of Algebra.This developed the principles of algebra.He derived general methods for solving cubic equations and equations with higher orders.Mohammad al-Khawarizmi:Muslim scientist from Persia.Adapted Ptolemy’s Geographike Hyphegesis [Geographic Guidance].Wrote the first book in arabic on figure reckoning.Used indian and Greek sources, and a Euclidean geometrical method.“Father of Algebra”; “algorithm”.Kitab Al-Jabr wa Al-Muwabalahat the end of the 12thcentury.Al Hassan Ibn al-Haytham:Muslim scientist of Arab origin [most likely Egyptian].Contributed to mathematics and physics, particularly optics. He wrote Kitab al Manazir [Book of Optics] where he formulated “Alhazen’sproblem” – for any two points opposite a reflecting surface to find the point(s) on the surface at which the light from one of the two points will bereflected to the other. This book discusses vision and light, and the basic idea of a camera comesfrom this book. Hisab: the art of reckoning. Three different systems were inherited by the Arabs:1.Finger reckoning: numbers expressed in words, not in symbols. Also known asthe arithmetic of the scribes. Counting by fingers2.Figure reckoning: came from India. Able to express any number by means of nine figures and a symbol  indicating an empty place in an array of figures.
First transmitted to Europe through a translation of al-Khwarizmi. One figure to represent the number. Ex: 4 not I I I I.