Author(s): Arthur Mazer
Publisher: Wiley
Year: 2010
Language: English
Pages: 315
Tags: Математика;История математики;
CONTENTS
......Page 6
PREFACE
......Page 10
1 INTRODUCTION
......Page 13
2.1 A STICKY MATTER......Page 17
2.2 NUMBERS......Page 54
CHAPTER 3 THE SPACE: GEOMETRY......Page 74
3.1 EUCLIDEAN SPACE, DIMENSION AND RESCALING......Page 76
3.2 MEASUREMENTS OF VARIOUS OBJECTS......Page 84
CHAPTER 4 THE LANGUAGE: ALGEBRA......Page 108
4.1 CARTESIAN COORDINATES AND TRANSLATIONOF THE AX......Page 113
4.2 POLYNOMIALS......Page 118
4.3 CIRCLES......Page 125
4.4 THE FOUR-DIMENSIONAL SPHERE......Page 133
4.5 FINITE SERIES AND INDUCTION......Page 141
4.6 LINEAR ALGEBRA IN TWO DIMENSIONS......Page 145
4.7 THE ELLIPSE......Page 162
CHAPTER 5 THE UNIVERSAL TOOL: TRIGONOMETRY......Page 168
5.1 TRIGONOMETRIC FUNCTIONS......Page 170
5.3 ROTATIONS......Page 177
5.4 IDENTITIES......Page 179
5.5 LUCKY 72......Page 182
5.6 PTOLEMY AND ARISTARCHUS......Page 185
5.7 DRAWING A PENTAGON......Page 193
5.8 POLAR COORDINATES......Page 195
5.9 THE DETERMINANT......Page 200
CHAPTER 6 THE SLAYER: CALCULUS......Page 204
6.1 STUDIES OF MOTION AND THE FUNDAMENTAL THEOREM OF CALCULUS......Page 211
6.2 MORE MOTION: GOING IN CIRCLES......Page 225
6.3 MORE DIFFERENTIAL CALCULUS......Page 229
6.4 MORE INTEGRAL CALCULUS......Page 246
6.5 POTPOURRI......Page 254
CHAPTER 7 EIGHT MINUTES THAT CHANCED HISTORY......Page 261
7.1 NEWTON'S LAWS OF MOTION......Page 277
7.2 GALILEAN CHECKPOINT......Page 280
7.3 CONSTANTS OF MOTION AND ENERGY......Page 284
7.4 KEPLER AND NEWTON; ARISTARCHUS REDEEMED......Page 287
EPILOGUE
......Page 307
BIBLIOGRAPHY
......Page 309
INDEX......Page 311
