Episodes in the Mathematics of Medieval Islam

Name: Episodes in the Mathematics of Medieval Islam
Brand: Springer
Price: 64.19 EUR
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J.L. Berggren(Autor*in)

Springer (Verlag)

1. Auflage

Erschienen am 25. November 2014

XIV, 197 Seiten

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Beschreibung

This book presents episodes from the mathematics of medieval Islam, work which has had a great impact on the development of mathematics. The author describes the subject in its proper historical context, referring to specific Arabic texts. Among the topics discussed are decimal arithmetic, plane and spherical trigonometry, algebra, interpolation and approximation of roots of equations. This book should be of great interest to historians of mathematics, as well as to students of mathematics. The presentation is readily accessible to anyone with a background in high school mathematics.

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From the reviews:

J.L. Berggren

Episodes in the Mathematics of Medieval Islam

"[The] first book of its kind . . . Very interesting. It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arabic mathematics. None of them is pursued to exhaustion, but all of them arranged in such a way, together with accompanying exercises, so that they would engage an active mind and introduce a subject."

-ZENTRALBLATT MATH

"This is a most scholarly book. The presentation is in the style of a textbook; each of the six chapters being followed by a set of exercises and a bibliography. . There is a good table of contents and a comprehensive index. . This is an excellent book full of information and thought-provoking ideas. It is worthy of careful study which will lead to a greater understanding of what the Islamic world has contributed to mathematics." (D.Stander, The Mathematical Gazette, Vol. 89 (515), 2005)

"Written in 1986 and inspired by Asger Aaboe's classic Episodes in the Early History of Mathematics, this book contains a wealth of classroom-ready examples of much of the mathematics one finds in high school and early college . . Springer has taken the right step by issuing a paperback edition to get the book into the hands of a more general readership. . The re-issue of this gem is significant and welcomed. It will enrich your classes and deepen your perspective on mathematics and culture." (Glen van Brummelen, The MAA Mathematical Sciences Digital Library, January, 2004)

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Inhalt

1. Introduction.- §1. The Beginnings of Islam.- §2. Islam's Reception of Foreign Science.- §3. Four Muslim Scientists.- §4. The Sources.- §5. The Arabic Language and Arabic Names.- Exercises.- 2. Islamic Arithmetic.- §1. The Decimal System.- §2. K?shy?r's Arithmetic.- §3. The Discovery of Decimal Fractions.- §4. Muslim Sexagesimal Arithmetic.- §5. Square Roots.- §6. Al-K?sh?'s Extraction of a Fifth Root.- §7. The Islamic Dimension: Problems of Inheritance.- Exercises.- 3. Geometrical Constructions in the Islamic World.- §1. Euclidean Constructions.- §2. Greek Sources for Islamic Geometry.- §3. Apollonios' Theory of the Conics.- §4. Ab? Sahl on the Regular Heptagon.- §5. The Construction of the Regular Nonagon.- §6. Construction of the Conic Sections.- §7. The Islamic Dimension: Geometry with a Rusty Compass.- Exercises.- 4. Algebra in Islam.- §1. Problems About Unknown Quantities.- §2. Sources of Islamic Algebra.- §3. Al-Khw?rizm?'s Algebra.- §4. Thabit's Demonstration for Quadratic Equations.- §5. Ab? K?mil on Algebra.- §6. Al-Karaj?'s Arithmetization of Algebra.- §7. 'Umar al-Khayy?m? and the Cubic Equation.- §8. The Islamic Dimension: The Algebra of Legacies.- Exercises.- 5. Trigonometry in the Islamic World.- §1. Ancient Background: The Table of Chords and the Sine.- §2. The Introduction of the Six Trigonometric Functions.- §3. Abu l-Waf?'s Proof of the Addition Theorem for Sines.- §4. Nas?r al-D?n's Proof of the Sine Law.- §5. Al-B?r?n?'s Measurement of the Earth.- §6. Trigonometric Tables: Calculation and Interpolation.- §7. Auxiliary Functions.- §8. Interpolation Procedures.- §9. Al-K?sh?'s Approximation to Sin(1°).- Exercises.- 6. Spherics in the Islamic World.- §1. The AncientBackground.- §2. Important Circles on the Celestial Sphere.- §3. The Rising Times of the Zodiacal Signs.- §4. Stereographic Projection and the Astrolabe.- §5. Telling Time by Sun and Stars.- §6. Spherical Trigonometry in Islam.- §7. Tables for Spherical Astronomy.- §8. The Islamic Dimension: The Direction of Prayer.- Exercises.

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