UID:
almahu_9947362986702882
Umfang:
XIV, 197 p. 18 illus.
,
online resource.
ISBN:
9781461246084
Inhalt:
From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens Høyrup, Mathematical Reviews ...as a textbook, this work is highly commendable...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, which I am sure the author agrees with me is, at this stage, very difficult to introduce. - G.Saliba, Zentralblatt.
Anmerkung:
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 Ancient Background -- §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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9780387406053
Sprache:
Englisch
DOI:
10.1007/978-1-4612-4608-4
URL:
http://dx.doi.org/10.1007/978-1-4612-4608-4
