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Computing with Real Numbers, from Archimedes to Turing and Beyond
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Kapitel in diesem Buch
- Frontmatter i
- Contents vii
- Introduction ix
- Mathematics and the Good Life 1
- The Rise of Big Data: How It’s Changing the Way We Think about the World 20
- Conway’s Wizards 33
- On Unsettleable Arithmetical Problems 39
- Crinkly Curves 49
- Why Do We Perceive Logarithmically? 64
- The Music of Math Games 74
- The Fundamental Theorem of Algebra for Artists 87
- The Arts—Digitized, Quantified, and Analyzed 96
- On the Number of Klein Bottle Types 105
- Adventures in Mathematical Knitting 128
- The Mathematics of Fountain Design: A Multiple-Centers Activity 144
- Food for (Mathematical) Thought 156
- Wondering about Wonder in Mathematics 165
- The Lesson of Grace in Teaching 188
- Generic Proving: Reflections on Scope and Method 198
- Extreme Proofs I: The Irrationality of √2 216
- Stuck in the Middle: Cauchy’s Intermediate Value Theorem and the History of Analytic Rigor 228
- Plato, Poincaré, and the Enchanted Dodecahedron: Is the Universe Shaped Like the Poincaré Homology Sphere? 239
- Computing with Real Numbers, from Archimedes to Turing and Beyond 251
- Chaos at Fifty 270
- Twenty-Five Analogies for Explaining Statistical Concepts 288
- College Admissions and the Stability of Marriage 299
- The Beauty of Bounded Gaps 308
- Contributors 315
- Notable Writings 325
- Acknowledgments 333
- Credits 335
Kapitel in diesem Buch
- Frontmatter i
- Contents vii
- Introduction ix
- Mathematics and the Good Life 1
- The Rise of Big Data: How It’s Changing the Way We Think about the World 20
- Conway’s Wizards 33
- On Unsettleable Arithmetical Problems 39
- Crinkly Curves 49
- Why Do We Perceive Logarithmically? 64
- The Music of Math Games 74
- The Fundamental Theorem of Algebra for Artists 87
- The Arts—Digitized, Quantified, and Analyzed 96
- On the Number of Klein Bottle Types 105
- Adventures in Mathematical Knitting 128
- The Mathematics of Fountain Design: A Multiple-Centers Activity 144
- Food for (Mathematical) Thought 156
- Wondering about Wonder in Mathematics 165
- The Lesson of Grace in Teaching 188
- Generic Proving: Reflections on Scope and Method 198
- Extreme Proofs I: The Irrationality of √2 216
- Stuck in the Middle: Cauchy’s Intermediate Value Theorem and the History of Analytic Rigor 228
- Plato, Poincaré, and the Enchanted Dodecahedron: Is the Universe Shaped Like the Poincaré Homology Sphere? 239
- Computing with Real Numbers, from Archimedes to Turing and Beyond 251
- Chaos at Fifty 270
- Twenty-Five Analogies for Explaining Statistical Concepts 288
- College Admissions and the Stability of Marriage 299
- The Beauty of Bounded Gaps 308
- Contributors 315
- Notable Writings 325
- Acknowledgments 333
- Credits 335