Mathematical fallacies, flaws, and flimflam:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, DC
Mathematical Association of America
[2000]
|
| Schriftenreihe: | MAA spectrum
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Print version record |
| Beschreibung: | 1 online resource (xvi, 167 pages) illustrations |
| ISBN: | 9781614445180 1614445184 0883855291 9780883855294 |
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| 100 | 1 | |a Barbeau, Edward |d 1938- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical fallacies, flaws, and flimflam |c Edward J. Barbeau |
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| 505 | 8 | |a Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining | |
| 505 | 8 | |a ""Copyright page ""; ""title page ""; ""FOREWORD""; ""Contents""; ""1 NUMBERS""; ""1. How to get drunk and rich at the same time""; ""2. Fifty per cent more for fifty per cent less""; ""3. Whose real world?""; ""4. United in purpose""; ""5. A case of black and white -- but not so much black""; ""6. Effects of changing temperature""; ""7. To those that have shall be given""; ""8. Distributing addition over multiplication""; ""9. Distributing exponents over sums""; ""10. An exponential mess""; ""11. A product of logarithms""; ""12. A divisibility property""; ""13. All perfect numbers are even"" | |
| 505 | 8 | |a ""14. Why Wiles' proof of the Fermat Conjecture is false""""15. A quick (?) proof of irrationality""; ""16. A rational combination of two transcendentals""; ""17. How the factorial works""; ""Dollars and sense""; ""2 ALGEBRA AND TRIGONOMETRY""; ""1. Do you know how to split the atom?""; ""2. The number of tickets""; ""3. A superficial volume problem""; ""4. The end justifies the means""; ""5. How to solve a quadratic equation""; ""6. A new method for solving a cubic""; ""7. An old method for solving a cubic""; ""8. An exponential equation""; ""9. Logarithms distribute over sums"" | |
| 505 | 8 | |a ""10. The multiplication rules for logarithms""""11. A lack of technical unanimity""; ""12. A straightforward cancellation""; ""13. An application of the Cauchy-Schwarz Inequality""; ""14. Surprising symmetry""; ""15. Factoring homogeneous polynomials""; ""16. Polynomial detection""; ""17. The remainder theorem""; ""18. The zero polynomial""; ""19. An inductive fallacy""; ""20. On not identifying equations and identities""; ""21. A surd equation""; ""22. The disappearing solution""; ""23. Solving an inequality""; ""24. An appearance of finite geometric sequences"" | |
| 505 | 8 | |a ""25. Glide-reflecting the sine curve""""26. A trigonometric identity""; ""27. Floored by an Olympiad problem""; ""28. A New Identity for the Ceiling Function""; ""3 GEOMETRY""; ""1. The impossibility of angle bisection""; ""2. Trisecting an angle with ruler and compasses""; ""3. A luney way to square a circle""; ""4. The Steiner-Lehmus Theorem""; ""5. A geometry problem""; ""6. A case of irregularity""; ""7. A counterexample to Morley's Theorem""; ""8. Going for the stars""; ""9. Identifying the angle""; ""10. The speeder's delight""; ""11. A solution to problem 480"" | |
| 505 | 8 | |a ""12. Tangency by double roots""""13. A puzzling graph""; ""14. The wilting lines""; ""15. The height of a trapezoid""; ""16. Forces with a given resultant""; ""17. A linear pythagorean theorem""; ""18. The surface area of a sphere""; ""19. Drenching a sphere""; ""20. Volume of a tin can""; ""21. The Puptent Problem""; ""22. The spirit is willing but the ham is rotten""; ""4 FINITE MATHEMATICS""; ""1. Rabbits reproduce; integers don't""; ""2. All positive integers are equal""; ""3. Every second square is the same""; ""4. Four weighings suffice""; ""5. Perron's paradox"" | |
| 650 | 4 | |a Errors, scientific | |
| 650 | 4 | |a Mathématiques / Miscellanées | |
| 650 | 7 | |a MATHEMATICS / Essays |2 bisacsh | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Barbeau, Edward, 1938- |t Mathematical fallacies, flaws, and flimflam |
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Datensatz im Suchindex
| _version_ | 1804176608262619136 |
|---|---|
| any_adam_object | |
| author | Barbeau, Edward 1938- |
| author_facet | Barbeau, Edward 1938- |
| author_role | aut |
| author_sort | Barbeau, Edward 1938- |
| author_variant | e b eb |
| building | Verbundindex |
| bvnumber | BV043779482 |
| collection | ZDB-4-EBA |
| contents | Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining ""Copyright page ""; ""title page ""; ""FOREWORD""; ""Contents""; ""1 NUMBERS""; ""1. How to get drunk and rich at the same time""; ""2. Fifty per cent more for fifty per cent less""; ""3. Whose real world?""; ""4. United in purpose""; ""5. A case of black and white -- but not so much black""; ""6. Effects of changing temperature""; ""7. To those that have shall be given""; ""8. Distributing addition over multiplication""; ""9. Distributing exponents over sums""; ""10. An exponential mess""; ""11. A product of logarithms""; ""12. A divisibility property""; ""13. All perfect numbers are even"" ""14. Why Wiles' proof of the Fermat Conjecture is false""""15. A quick (?) proof of irrationality""; ""16. A rational combination of two transcendentals""; ""17. How the factorial works""; ""Dollars and sense""; ""2 ALGEBRA AND TRIGONOMETRY""; ""1. Do you know how to split the atom?""; ""2. The number of tickets""; ""3. A superficial volume problem""; ""4. The end justifies the means""; ""5. How to solve a quadratic equation""; ""6. A new method for solving a cubic""; ""7. An old method for solving a cubic""; ""8. An exponential equation""; ""9. Logarithms distribute over sums"" ""10. The multiplication rules for logarithms""""11. A lack of technical unanimity""; ""12. A straightforward cancellation""; ""13. An application of the Cauchy-Schwarz Inequality""; ""14. Surprising symmetry""; ""15. Factoring homogeneous polynomials""; ""16. Polynomial detection""; ""17. The remainder theorem""; ""18. The zero polynomial""; ""19. An inductive fallacy""; ""20. On not identifying equations and identities""; ""21. A surd equation""; ""22. The disappearing solution""; ""23. Solving an inequality""; ""24. An appearance of finite geometric sequences"" ""25. Glide-reflecting the sine curve""""26. A trigonometric identity""; ""27. Floored by an Olympiad problem""; ""28. A New Identity for the Ceiling Function""; ""3 GEOMETRY""; ""1. The impossibility of angle bisection""; ""2. Trisecting an angle with ruler and compasses""; ""3. A luney way to square a circle""; ""4. The Steiner-Lehmus Theorem""; ""5. A geometry problem""; ""6. A case of irregularity""; ""7. A counterexample to Morley's Theorem""; ""8. Going for the stars""; ""9. Identifying the angle""; ""10. The speeder's delight""; ""11. A solution to problem 480"" ""12. Tangency by double roots""""13. A puzzling graph""; ""14. The wilting lines""; ""15. The height of a trapezoid""; ""16. Forces with a given resultant""; ""17. A linear pythagorean theorem""; ""18. The surface area of a sphere""; ""19. Drenching a sphere""; ""20. Volume of a tin can""; ""21. The Puptent Problem""; ""22. The spirit is willing but the ham is rotten""; ""4 FINITE MATHEMATICS""; ""1. Rabbits reproduce; integers don't""; ""2. All positive integers are equal""; ""3. Every second square is the same""; ""4. Four weighings suffice""; ""5. Perron's paradox"" |
| ctrlnum | (ZDB-4-EBA)ocn860712676 (OCoLC)860712676 (DE-599)BVBBV043779482 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043779482 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:34:53Z |
| institution | BVB |
| isbn | 9781614445180 1614445184 0883855291 9780883855294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029190542 |
| oclc_num | 860712676 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (xvi, 167 pages) illustrations |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Mathematical Association of America |
| record_format | marc |
| series2 | MAA spectrum |
| spelling | Barbeau, Edward 1938- Verfasser aut Mathematical fallacies, flaws, and flimflam Edward J. Barbeau Washington, DC Mathematical Association of America [2000] © 2000 1 online resource (xvi, 167 pages) illustrations txt rdacontent c rdamedia cr rdacarrier MAA spectrum Print version record Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining ""Copyright page ""; ""title page ""; ""FOREWORD""; ""Contents""; ""1 NUMBERS""; ""1. How to get drunk and rich at the same time""; ""2. Fifty per cent more for fifty per cent less""; ""3. Whose real world?""; ""4. United in purpose""; ""5. A case of black and white -- but not so much black""; ""6. Effects of changing temperature""; ""7. To those that have shall be given""; ""8. Distributing addition over multiplication""; ""9. Distributing exponents over sums""; ""10. An exponential mess""; ""11. A product of logarithms""; ""12. A divisibility property""; ""13. All perfect numbers are even"" ""14. Why Wiles' proof of the Fermat Conjecture is false""""15. A quick (?) proof of irrationality""; ""16. A rational combination of two transcendentals""; ""17. How the factorial works""; ""Dollars and sense""; ""2 ALGEBRA AND TRIGONOMETRY""; ""1. Do you know how to split the atom?""; ""2. The number of tickets""; ""3. A superficial volume problem""; ""4. The end justifies the means""; ""5. How to solve a quadratic equation""; ""6. A new method for solving a cubic""; ""7. An old method for solving a cubic""; ""8. An exponential equation""; ""9. Logarithms distribute over sums"" ""10. The multiplication rules for logarithms""""11. A lack of technical unanimity""; ""12. A straightforward cancellation""; ""13. An application of the Cauchy-Schwarz Inequality""; ""14. Surprising symmetry""; ""15. Factoring homogeneous polynomials""; ""16. Polynomial detection""; ""17. The remainder theorem""; ""18. The zero polynomial""; ""19. An inductive fallacy""; ""20. On not identifying equations and identities""; ""21. A surd equation""; ""22. The disappearing solution""; ""23. Solving an inequality""; ""24. An appearance of finite geometric sequences"" ""25. Glide-reflecting the sine curve""""26. A trigonometric identity""; ""27. Floored by an Olympiad problem""; ""28. A New Identity for the Ceiling Function""; ""3 GEOMETRY""; ""1. The impossibility of angle bisection""; ""2. Trisecting an angle with ruler and compasses""; ""3. A luney way to square a circle""; ""4. The Steiner-Lehmus Theorem""; ""5. A geometry problem""; ""6. A case of irregularity""; ""7. A counterexample to Morley's Theorem""; ""8. Going for the stars""; ""9. Identifying the angle""; ""10. The speeder's delight""; ""11. A solution to problem 480"" ""12. Tangency by double roots""""13. A puzzling graph""; ""14. The wilting lines""; ""15. The height of a trapezoid""; ""16. Forces with a given resultant""; ""17. A linear pythagorean theorem""; ""18. The surface area of a sphere""; ""19. Drenching a sphere""; ""20. Volume of a tin can""; ""21. The Puptent Problem""; ""22. The spirit is willing but the ham is rotten""; ""4 FINITE MATHEMATICS""; ""1. Rabbits reproduce; integers don't""; ""2. All positive integers are equal""; ""3. Every second square is the same""; ""4. Four weighings suffice""; ""5. Perron's paradox"" Errors, scientific Mathématiques / Miscellanées MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh MATHEMATICS / General bisacsh Mathematics fast Wiskunde gtt Fouten gtt Mathematik Mathematics Miscellanea Unterhaltungsmathematik (DE-588)4124357-2 gnd rswk-swf Unterhaltungsmathematik (DE-588)4124357-2 s 1\p DE-604 Erscheint auch als Druck-Ausgabe Barbeau, Edward, 1938- Mathematical fallacies, flaws, and flimflam 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barbeau, Edward 1938- Mathematical fallacies, flaws, and flimflam Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining ""Copyright page ""; ""title page ""; ""FOREWORD""; ""Contents""; ""1 NUMBERS""; ""1. How to get drunk and rich at the same time""; ""2. Fifty per cent more for fifty per cent less""; ""3. Whose real world?""; ""4. United in purpose""; ""5. A case of black and white -- but not so much black""; ""6. Effects of changing temperature""; ""7. To those that have shall be given""; ""8. Distributing addition over multiplication""; ""9. Distributing exponents over sums""; ""10. An exponential mess""; ""11. A product of logarithms""; ""12. A divisibility property""; ""13. All perfect numbers are even"" ""14. Why Wiles' proof of the Fermat Conjecture is false""""15. A quick (?) proof of irrationality""; ""16. A rational combination of two transcendentals""; ""17. How the factorial works""; ""Dollars and sense""; ""2 ALGEBRA AND TRIGONOMETRY""; ""1. Do you know how to split the atom?""; ""2. The number of tickets""; ""3. A superficial volume problem""; ""4. The end justifies the means""; ""5. How to solve a quadratic equation""; ""6. A new method for solving a cubic""; ""7. An old method for solving a cubic""; ""8. An exponential equation""; ""9. Logarithms distribute over sums"" ""10. The multiplication rules for logarithms""""11. A lack of technical unanimity""; ""12. A straightforward cancellation""; ""13. An application of the Cauchy-Schwarz Inequality""; ""14. Surprising symmetry""; ""15. Factoring homogeneous polynomials""; ""16. Polynomial detection""; ""17. The remainder theorem""; ""18. The zero polynomial""; ""19. An inductive fallacy""; ""20. On not identifying equations and identities""; ""21. A surd equation""; ""22. The disappearing solution""; ""23. Solving an inequality""; ""24. An appearance of finite geometric sequences"" ""25. Glide-reflecting the sine curve""""26. A trigonometric identity""; ""27. Floored by an Olympiad problem""; ""28. A New Identity for the Ceiling Function""; ""3 GEOMETRY""; ""1. The impossibility of angle bisection""; ""2. Trisecting an angle with ruler and compasses""; ""3. A luney way to square a circle""; ""4. The Steiner-Lehmus Theorem""; ""5. A geometry problem""; ""6. A case of irregularity""; ""7. A counterexample to Morley's Theorem""; ""8. Going for the stars""; ""9. Identifying the angle""; ""10. The speeder's delight""; ""11. A solution to problem 480"" ""12. Tangency by double roots""""13. A puzzling graph""; ""14. The wilting lines""; ""15. The height of a trapezoid""; ""16. Forces with a given resultant""; ""17. A linear pythagorean theorem""; ""18. The surface area of a sphere""; ""19. Drenching a sphere""; ""20. Volume of a tin can""; ""21. The Puptent Problem""; ""22. The spirit is willing but the ham is rotten""; ""4 FINITE MATHEMATICS""; ""1. Rabbits reproduce; integers don't""; ""2. All positive integers are equal""; ""3. Every second square is the same""; ""4. Four weighings suffice""; ""5. Perron's paradox"" Errors, scientific Mathématiques / Miscellanées MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh MATHEMATICS / General bisacsh Mathematics fast Wiskunde gtt Fouten gtt Mathematik Mathematics Miscellanea Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| subject_GND | (DE-588)4124357-2 |
| title | Mathematical fallacies, flaws, and flimflam |
| title_auth | Mathematical fallacies, flaws, and flimflam |
| title_exact_search | Mathematical fallacies, flaws, and flimflam |
| title_full | Mathematical fallacies, flaws, and flimflam Edward J. Barbeau |
| title_fullStr | Mathematical fallacies, flaws, and flimflam Edward J. Barbeau |
| title_full_unstemmed | Mathematical fallacies, flaws, and flimflam Edward J. Barbeau |
| title_short | Mathematical fallacies, flaws, and flimflam |
| title_sort | mathematical fallacies flaws and flimflam |
| topic | Errors, scientific Mathématiques / Miscellanées MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh MATHEMATICS / General bisacsh Mathematics fast Wiskunde gtt Fouten gtt Mathematik Mathematics Miscellanea Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| topic_facet | Errors, scientific Mathématiques / Miscellanées MATHEMATICS / Essays MATHEMATICS / Pre-Calculus MATHEMATICS / Reference MATHEMATICS / General Mathematics Wiskunde Fouten Mathematik Mathematics Miscellanea Unterhaltungsmathematik |
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