. The birth of mathematics: ancient times to 1300

Cover......Page 1
Title -- THE BIRTH OF MATHEMATICS: Ancient Times to 1300......Page 2
Copyright......Page 3
Contents......Page 4
Preface......Page 8
Acknowledgments......Page 10
Introduction......Page 12
1. Thales of Miletus (ca. 625–ca. 547 B.C.E.): Earliest Proofs of Geometrical Theorems......Page 14
Natural Philosopher......Page 15
First Proofs of Theorems in Mathematics......Page 16
Discoveries in Astronomy......Page 19
Ingenious Solutions to Practical Problems......Page 21
Legends about Thales......Page 23
Conclusion......Page 24
FURTHER READING......Page 25
2. Pythagoras of Samos (ca. 560–ca. 480 B.C.E.): Ancient Greek Proves Theorem about\rRight Triangles......Page 27
First Student is Paid to Learn......Page 28
Pythagorean Society Blends Mysticism with Mathematics......Page 29
Early Research in Number Theory......Page 30
Ratios in Music and Astronomy......Page 33
Pythagorean Theorem......Page 34
Irrational Numbers......Page 36
Five Regular Solids......Page 38
Conclusion......Page 40
FURTHER READING......Page 41
3. Euclid of Alexandria (ca. 325–ca. 270 B.C.E.): Geometer Who Organized Mathematics......Page 42
Professor of Mathematics......Page 43
Elements......Page 44
Original Results in Elements......Page 46
Criticisms of Euclid’s Methods......Page 48
Parallel Postulate......Page 49
Euclid’s Additional Writings......Page 51
Conclusion......Page 53
FURTHER READING......Page 54
4. Archimedes of Syracuse (ca. 287–212 B.C.E.): Innovator of Techniques in Geometry......Page 56
Inventor of Practical Machines......Page 57
Approximation of Pi Using Inscribed and Circumscribed Polygons......Page 59
Method of Exhaustion to Estimate Areas and Volumes......Page 61
Creative Problem-Solver......Page 64
Investigations of Large Numbers......Page 66
Conclusion......Page 68
FURTHER READING......Page 69
5. Hypatia of Alexandria (ca. 370–415 C.E.): First Woman of Mathematics......Page 70
The “Perfect” Human Being......Page 71
Commentaries on Classical Mathematics Books......Page 72
Famous Teacher, Philosopher, and Scientist......Page 75
Brutally Murdered......Page 76
FURTHER READING......Page 78
6. Aryabhata I (476–550 C.E.): From Alphabetical Numbers to the Rotation of the Earth......Page 80
Aryabhatiya (Aryabhata’s Treatise)......Page 81
Arithmetical Methods......Page 82
Geometric Techniques......Page 84
Tables of Sines......Page 86
Astronomical Theories......Page 88
Conclusion......Page 90
FURTHER READING......Page 91
7. Brahmagupta (598–668 C.E.): Father of Numerical Analysis......Page 92
Brahmasphutasiddhanta (Improved Astronomical System of Brahma)......Page 93
Arithmetical Innovations......Page 95
New Geometrical Techniques......Page 97
Algebraic Methods......Page 99
Second Astronomical Treatise......Page 102
Conclusion......Page 103
FURTHER READING......Page 104
8. Abu Ja‘far Muhammad ibn Musa al-Khwarizmi (ca. 800–ca. 847 C.E.): Father of Algebra......Page 105
Text on Algebra......Page 106
Text on Arithmetic......Page 110
Astronomical Tables......Page 112
Geographical Work......Page 113
Minor Works......Page 114
FURTHER READING......Page 115
9. Omar Khayyam (ca. 1048–ca. 1131 C.E.): Mathematician, Astronomer, Philosopher, and Poet......Page 117
Early Years......Page 118
Early Writings on Arithmetic, Algebra, and Music......Page 119
Geometrical Solutions of Cubic Equations......Page 121
Calendar Reform......Page 122
Parallel Lines and Ratios......Page 123
Philosophical Writings......Page 124
Rubáiyát (Quatrains)......Page 125
Conclusion......Page 127
FURTHER READING......Page 128
10. Leonardo Fibonacci (ca. 1175–ca. 1250 C.E.): Hindu-Arabic Numerals in Europe......Page 130
Hindu-Arabic Numbering System......Page 131
Liber Abaci (Book of Computation)......Page 133
Fibonacci Series......Page 135
Mathematical Tournament......Page 136
Liber Quadratorum (Book of the Square)......Page 138
Conclusion......Page 139
FURTHER READING......Page 140
Glossary......Page 142
Further Reading......Page 152
Associations......Page 157
Index......Page 158