The legacy of Martin Gardner is celebrated in this broad collection of articles. Essential reading for all recreational mathematicians. Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau's previous book, material is drawn from a variety of sources including the work of students, textbooks, the media, and professional mathematicians.
The legacy of Martin Gardner is celebrated in this broad collection of articles. Essential reading for all recreational mathematicians.Mistakes in mathematical reasoning can range from outlandish blunders to deep and subtle oversights that evade even the most watchful eye. This book represents the second collection of such errors to be compiled by Edward Barbeau. Like Barbeau's previous book, material is drawn from a variety of sources including the work of students, textbooks, the media, and professional mathematicians.
Preface Part I. Geometry: 1. The asymmetric propeller Martin Gardner 2. The asymmetric propeller revisited Gillian Saenz, Christopher Jackson, and Ryan Crumley 3. Bracing regular polygons as we race into the future Greg W. Frederickson 4. A Platonic Sextet for Strings Karl Schaffer 5. Prince Rupert's rectangles Richard P. Jerrard and John E. Wetzel Part II. Number Theory and Graph Theory: 6. Transcendentals and early birds Martin Gardner 7. Squaring, cubing, and cube rooting Arthur T. Benjamin 8. Carryless arithmetic mod 10 David Applegate, Marc LeBrun and N. J. A. Sloane 9. Mad tea party cyclic partitions Robert Bekes, Jean Pedersen and Bin Sha 10. The continuing saga of snarks Sarah-Marie Belcastro 11. The map-coloring game Tomasz Bartnicki, Jaroslaw Grytczuk, H. A. Kierstead and Xuding Zhu Part III. Flexagons and Catalan Numbers: 12. It's okay to be square If you're a flexagon Ethan J. Berkove and Jeffrey P. Dumont 13. The V-flex, triangle orientation, and Catalan numbers in hexaflexagons Ionut E. Iacob, T. Bruce McLean and Hua Wang 14. From hexaflexagons to edge flexagons to point flexagons Les Pook 15. Flexagons lead to a Catalan number identity David Callan 16. Convergence of a Catalan series Thomas Koshy and Z. Gao Part IV. Making Things Fit: 17. L-tromino tiling of mutilated chessboards Martin Gardner 18. Polyomino dissections Tiina Hohn and Andy Liu 19. Squaring the plane Frederick V. Henle and James M. Henle 20. Magic knight's tours John Beasley 21. Some new results on magic hexagrams Martin Gardner 22. Finding all solutions to the magic hexagram Alexander Karabegov and Jason Holland 23. Triangular numbers, Gaussian integers, and KenKen John J. Watkins Part V. Further Puzzles and Games 24. Cups and downs Ian Stewart 25. 30 years of Bulgarian solitaire Brian Hopkins 26. Congo bongo Hsin-Po Wang 27. Sam Loyd's courier problem with Diophantus, Pythagoras, and Martin Gardner Owen O'Shea 28. Retrolife and the pawns neighbors Yossi Elran 29. RATWYT Aviezri Fraenkel Part VI. Cards and Probability 30. Modeling mathematics with playing cards Martin Gardner 31. The probability an amazing card trick is dull Christopher N. Swanson 32. The Monty Hall problem, reconsidered Stephen Lucas, Jason Rosenhouse and Andrew Schepler 33. The secretary problem from the applicant's point of view Darren Glass 34. Lake Wobegon dice Jorge Moraleda and David G. Stork 35. Martin Gardner's mistake Tanya Khovanova Part VII. Other Aspects of Martin Gardner: 36. Against the odds Martin Gardner 37. A modular miracle John Stillwell 38. The golden ratio-a contrary viewpoint Clement Falbo 39. Review of The Mysterious Mr. Ammann by Marjorie Senechal Philip Straffin 40. Review of PopCo by Scarlett Thomas Martin Gardner 41. Superstrings and Thelma Martin Gardner Index About the editors.
Preface Part I. Geometry: 1. The asymmetric propeller Martin Gardner 2. The asymmetric propeller revisited Gillian Saenz, Christopher Jackson, and Ryan Crumley 3. Bracing regular polygons as we race into the future Greg W. Frederickson 4. A Platonic Sextet for Strings Karl Schaffer 5. Prince Rupert's rectangles Richard P. Jerrard and John E. Wetzel Part II. Number Theory and Graph Theory: 6. Transcendentals and early birds Martin Gardner 7. Squaring, cubing, and cube rooting Arthur T. Benjamin 8. Carryless arithmetic mod 10 David Applegate, Marc LeBrun and N. J. A. Sloane 9. Mad tea party cyclic partitions Robert Bekes, Jean Pedersen and Bin Sha 10. The continuing saga of snarks Sarah-Marie Belcastro 11. The map-coloring game Tomasz Bartnicki, Jaroslaw Grytczuk, H. A. Kierstead and Xuding Zhu Part III. Flexagons and Catalan Numbers: 12. It's okay to be square If you're a flexagon Ethan J. Berkove and Jeffrey P. Dumont 13. The V-flex, triangle orientation, and Catalan numbers in hexaflexagons Ionut E. Iacob, T. Bruce McLean and Hua Wang 14. From hexaflexagons to edge flexagons to point flexagons Les Pook 15. Flexagons lead to a Catalan number identity David Callan 16. Convergence of a Catalan series Thomas Koshy and Z. Gao Part IV. Making Things Fit: 17. L-tromino tiling of mutilated chessboards Martin Gardner 18. Polyomino dissections Tiina Hohn and Andy Liu 19. Squaring the plane Frederick V. Henle and James M. Henle 20. Magic knight's tours John Beasley 21. Some new results on magic hexagrams Martin Gardner 22. Finding all solutions to the magic hexagram Alexander Karabegov and Jason Holland 23. Triangular numbers, Gaussian integers, and KenKen John J. Watkins Part V. Further Puzzles and Games 24. Cups and downs Ian Stewart 25. 30 years of Bulgarian solitaire Brian Hopkins 26. Congo bongo Hsin-Po Wang 27. Sam Loyd's courier problem with Diophantus, Pythagoras, and Martin Gardner Owen O'Shea 28. Retrolife and the pawns neighbors Yossi Elran 29. RATWYT Aviezri Fraenkel Part VI. Cards and Probability 30. Modeling mathematics with playing cards Martin Gardner 31. The probability an amazing card trick is dull Christopher N. Swanson 32. The Monty Hall problem, reconsidered Stephen Lucas, Jason Rosenhouse and Andrew Schepler 33. The secretary problem from the applicant's point of view Darren Glass 34. Lake Wobegon dice Jorge Moraleda and David G. Stork 35. Martin Gardner's mistake Tanya Khovanova Part VII. Other Aspects of Martin Gardner: 36. Against the odds Martin Gardner 37. A modular miracle John Stillwell 38. The golden ratio-a contrary viewpoint Clement Falbo 39. Review of The Mysterious Mr. Ammann by Marjorie Senechal Philip Straffin 40. Review of PopCo by Scarlett Thomas Martin Gardner 41. Superstrings and Thelma Martin Gardner Index About the editors.
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