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Professor Engel’s Marvelously Improbable Machines
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James Propp
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Chapters in this book
- Frontmatter i
- Contents vii
- Introduction ix
- Geometry v. Gerrymandering 1
- Slicing Sandwiches, States, and Solar Systems: Can Mathematical Tools Help Determine What Divisions Are Provably Fair? 12
- Does Mathematics Teach How to Think? 27
- Abstracting the Rubik’s Cube 43
- Topology-Disturbing Objects: A New Class of 3D Optical Illusion 53
- Mathematicians Explore Mirror Link between Two Geometric Worlds 74
- Professor Engel’s Marvelously Improbable Machines 81
- The On-Line Encyclopedia of Integer Sequences 90
- Mathematics for Big Data 120
- The Un(solv)able Problem 132
- The Mechanization of Mathematics 150
- Mathematics as an Empirical Phenomenon, Subject to Modeling 171
- Does 2 + 3 = 5? In Defense of a Near Absurdity 186
- Gregory’s Sixth Operation 195
- Kolmogorov Complexity and Our Search for Meaning: What Math Can Teach Us about Finding Order in our Chaotic Lives 208
- Ethics in Statistical Practice and Communication: Five Recommendations 214
- The Fields Medal Should Return to Its Roots 224
- The Erdős Paradox 232
- Contributors 241
- Notable Writings 251
- Acknowledgments 269
- Credits 271
Chapters in this book
- Frontmatter i
- Contents vii
- Introduction ix
- Geometry v. Gerrymandering 1
- Slicing Sandwiches, States, and Solar Systems: Can Mathematical Tools Help Determine What Divisions Are Provably Fair? 12
- Does Mathematics Teach How to Think? 27
- Abstracting the Rubik’s Cube 43
- Topology-Disturbing Objects: A New Class of 3D Optical Illusion 53
- Mathematicians Explore Mirror Link between Two Geometric Worlds 74
- Professor Engel’s Marvelously Improbable Machines 81
- The On-Line Encyclopedia of Integer Sequences 90
- Mathematics for Big Data 120
- The Un(solv)able Problem 132
- The Mechanization of Mathematics 150
- Mathematics as an Empirical Phenomenon, Subject to Modeling 171
- Does 2 + 3 = 5? In Defense of a Near Absurdity 186
- Gregory’s Sixth Operation 195
- Kolmogorov Complexity and Our Search for Meaning: What Math Can Teach Us about Finding Order in our Chaotic Lives 208
- Ethics in Statistical Practice and Communication: Five Recommendations 214
- The Fields Medal Should Return to Its Roots 224
- The Erdős Paradox 232
- Contributors 241
- Notable Writings 251
- Acknowledgments 269
- Credits 271
