The Nature and Power of Mathematics [NOOK Book]

Overview


This captivating book explains some of the most fascinating ideas of mathematics to nonspecialists. It focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. Numerous illustrations. 1993 edition.
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The Nature and Power of Mathematics

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Overview


This captivating book explains some of the most fascinating ideas of mathematics to nonspecialists. It focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. Numerous illustrations. 1993 edition.
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Product Details

  • ISBN-13: 9780486152158
  • Publisher: Dover Publications
  • Publication date: 2/19/2013
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 400
  • Sales rank: 1,379,254
  • File size: 27 MB
  • Note: This product may take a few minutes to download.

Table of Contents

Preface
1 Some Greek Mathematics 3
1.1 [phi] and Irrational Numbers: An Introduction to Greek Mathematics 3
1.2 Euclidean Geometry 19
1.3 Greek Mathematics and Kepler 42
2 Non-Euclidean Geometry 69
2.1 Formal Axiom Systems 69
2.2 Precursors to Non-Euclidean Geometry 84
2.3 Hyperbolic Geometry 100
2.4 Spherical Geometry 122
2.5 Models of Hyperbolic Geometry 143
2.6 The Geometry of the Universe 160
3 Number Theory 182
3.1 Prime Numbers 182
3.2 The Euclidean Algorithm 208
3.3 Congruence Arithmetic 220
3.4 The Little Fermat Theorem 238
4 Cryptography 249
4.1 Some Basic Methods of Cryptography 249
4.2 Public Key Cryptography 267
5 Fractals 284
5.1 Fractal Dimension 284
5.2 Iteration and Computers 314
5.3 Mandelbrot and Julia sets 339
Epilogue 377
Bibliography 379
Credits 383
Index 385
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