Episodes in the Mathematics of Medieval Islam - Livres de poche

EAN (ISBN-13): 9780387406053
ISBN (ISBN-10): 0387406050
Version reliée
Livre de poche
Date de parution: 2003
Editeur: Springer
211 Pages
Poids: 0,313 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-05-24T23:05:08+02:00 (Zurich)
Page de détail modifiée en dernier sur 2023-09-22T19:35:16+02:00 (Zurich)
ISBN/EAN: 0387406050

ISBN - Autres types d'écriture:
0-387-40605-0, 978-0-387-40605-3
Autres types d'écriture et termes associés:
Auteur du livre: lennart berggren, len
Titre du livre: seeing islam others saw, episodes the mathematics medieval islam

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Données de l'éditeur

Auteur: J.L. Berggren
Titre: Episodes in the Mathematics of Medieval Islam
Editeur: Springer; Springer US
197 Pages
Date de parution: 2003-12-04
New York; NY; US
Imprimé / Fabriqué en
Poids: 0,690 kg
Langue: Anglais
65,99 € (DE)

BC; Book; Hardcover, Softcover / Mathematik/Allgemeines, Lexika; Geschichte der Mathematik; function; approximation; proof; Mathematica; equation; Euclid; algebra; Calculation; theorem; mathematics; geometry; arithmetic; calculus; history of mathematics; B; History of Mathematical Sciences; Mathematics and Statistics; Mathematics, general; Mathematik; BC

1. Introduction.- §1. The Beginnings of Islam.- §2. Islam’s Reception of Foreign Science.- §3. Four Muslim Scientists.- Al-Khw?rizm?.- Al-B?r?n?.- ‘Umar al-Khayy?m?.- Al-K?sh?.- §4. The Sources.- §5. The Arabic Language and Arabic Names.- The Language.- Transliterating Arabic.- Arabic Names.- Exercises.- 2. Islamic Arithmetic.- §1. The Decimal System.- §2. K?shy?r’s Arithmetic.- Survey of The Arithmetic.- Addition.- Subtraction.- Multiplication.- Division.- §3. The Discovery of Decimal Fractions.- §4. Muslim Sexagesimal Arithmetic.- History of Sexagesimals.- Sexagesimal Addition and Subtraction.- Sexagesimal Multiplication.- Multiplication by Levelling.- Multiplication Tables.- Methods of Sexagesimal Multiplication.- Sexagesimal Division.- §5. Square Roots.- Obtaining Approximate Square Roots.- Justifying the Approximation.- Justifying the Fractional Part.- Justifying the Integral Part.- §6. Al-K?sh?’s Extraction of a Fifth Root.- Laying Out the Work.- The Procedure for the First Two Digits.- Justification for the Procedure.- The Remaining Procedure.- The Fractional Part of the Root.- §7. The Islamic Dimension: Problems of Inheritance.- The First Problem of Inheritance.- The Second Problem of Inheritance.- On the Calculation of Zak?t.- Exercises.- 3. Geometrical Constructions in the Islamic World.- §1. Euclidean Constructions.- §2. Greek Sources for Islamic Geometry.- §3. Apollonios’ Theory of the Conics.- Symptom of the Parabola.- Symptom of the Hyperbola.- §4. Ab? Sahl on the Regular Heptagon.- Archimedes’ Construction of the Regular Heptagon.- Ab? Sahl’s Analysis.- First Reduction: From Heptagon to Triangle.- Second Reduction: From Triangle to Division of Line Segment.- Third Reduction: From the Divided Line Segment to Conic Sections.- §5. The Construction of the Regular Nonagon.- Verging Constructions.- Fixed Versus Moving Geometry.- Ab? Sahl’s Trisection of the Angle.- §6. Construction of the Conic Sections.- Life of Ibr?h?m b. Sin?n.- Ibr?h?m b. Sin?n on the Parabola.- Ibr?h?m b. Sin?n on the Hyperbola.- §7. The Islamic Dimension: Geometry with a Rusty Compass.- Problem 1.- Problem 2.- Problem 3.- Problem 4.- Problem 5.- Exercises.- 4. Algebra in Islam.- §1. Problems About Unknown Quantities.- §2. Sources of Islamic Algebra.- §3. Al-Khw?rizm?’s Algebra.- The Name “Algebra”.- Basic Ideas in Al-Khw?rizm?’s Algebra.- Al-Khw?rizm?’s Discussion of x2 + 21 = 10x.- §4. Thabit’s Demonstration for Quadratic Equations.- Preliminaries.- Th?bit’s Demonstration.- §5. Ab? K?mil on Algebra.- Similarities with al-Khw?rizm?.- Advances Beyond al-Khw?rizm?.- A Problem from Ab? K?mil.- §6. Al-Karaj?’s Arithmetization of Algebra.- Al-Samaw’al on the Law of Exponents.- Al-Samaw’al on the Division of Polynomials.- The First Example.- The Second Example.- §7. ‘Umar al-Khayy?m? and the Cubic Equation.- The Background to ‘Umar’s Work.- ‘Umar’s Classification of Cubic Equations.- ‘Umar’s Treatment of x3 + mx = n.- Preliminaries.- The Main Discussion.- ‘Umar’s Discussion of the Number of Roots.- §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.- Linear Interpolation.- Ibn Y?nus’ Second-Order Interpolation Scheme.- §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.