A History Of Mathematics

By (author) Carl B. Boyer; By (author) Boyer Carl B.; By (author) Merzbach Uta C.
Short description/annotation:
The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind s relationship with numbers, shapes, and patterns.
Description:
The updated new edition of the classic and comprehensive guide to the history of mathematics

For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.

• Distills thousands of years of mathematics into a single, approachable volume
• Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present
• Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.

Whether you''re interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Table of contents:

Foreword by Isaac Asimov xi

Preface to the Third Edition xiii

Preface to the Second Edition xv

Preface to the First Edition xvii

1 Traces 1

Concepts and Relationships 1

Early Number Bases 3

Number Language and Counting 5

Spatial Relationships 6

2 Ancient Egypt 8

The Era and the Sources 8

Numbers and Fractions 10

Arithmetic Operations 12

“Heap” Problems 13

Geometric Problems 14

Slope Problems 18

Arithmetic Pragmatism 19

3 Mesopotamia 21

The Era and the Sources 21

Cuneiform Writing 22

Numbers and Fractions: Sexagesimals 23

Positional Numeration 23

Sexagesimal Fractions 25

Approximations 25

Tables 26

Equations 28

Measurements: Pythagorean Triads 31

 Polygonal Areas 35

Geometry as Applied Arithmetic 36

4 Hellenic Traditions 40

The Era and the Sources 40

Thales and Pythagoras 42

Numeration 52

Arithmetic and Logistic 55

Fifth-Century Athens 56

Three Classical Problems 57

Quadrature of Lunes 58

Hippias of Elis 61

Philolaus and Archytas of Tarentum 63

Incommensurability 65

Paradoxes of Zeno 67

Deductive Reasoning 70

Democritus of Abdera 72

Mathematics and the Liberal Arts 74

The Academy 74

Aristotle 88

5 Euclid of Alexandria 90

Alexandria 90

Lost Works 91

Extant Works 91

The Elements 93

6 Archimedes of Syracuse 109

The Siege of Syracuse 109

On the Equilibriums of Planes 110

On Floating Bodies 111

The Sand-Reckoner 112

Measurement of the Circle 113

On Spirals 113

Quadrature of the Parabola 115

On Conoids and Spheroids 116

On the Sphere and Cylinder 118

Book of Lemmas 120

Semiregular Solids and Trigonometry 121

The Method 122

7 Apollonius of Perge 127

Works and Tradition 127

Lost Works 128

Cycles and Epicycles 129

The Conics 130

8 Crosscurrents 142

Changing Trends 142

Eratosthenes 143

Angles and Chords 144

Ptolemy