Mythematics

Michael Huber is associate professor of mathematics at Muhlenberg College.

• List of Figures xiii foreword xv Chapter 1: The First Labor: The Nemean Lion 1 1.1 The Tasks 2 1.1.1 Shooting an Arrow 2 1.1.2 Hercules Closes the Cave Mouth 2 1.1.3 Exercise: Zeus Makes a Deal 3 1.2 The Solutions 3 1.2.1 Shooting an Arrow 3 1.2.2 Hercules Closes the Cave Mouth 6 1.2.3 Exercise: Zeus Makes a Deal 10 Chapter 2: The Second Labor: The Lernean Hydra 13 2.1 The Tasks 13 2.1.1 One Head Replaced by Two 14 2.1.2 Cauterizing the Hydra 14 2.2 The Solutions 15 2.2.1 One Head Replaced by Two 15 2.2.2 Cauterizing the Hydra 17 Chapter 3: The Third Labor: The Hind of Ceryneia 20 3.1 The Tasks 20 3.1.1 Optimizing the Hind's Journey 21 3.1.2 Cerynitian Work 21 3.1.3 Exercise: Work with a Variable Force 21 3.2 The Solutions 22 3.2.1 Optimizing the Hind's Journey 22 3.2.2 Cerynitian Work 26 3.2.3 Exercise: Work with a Variable Force 27 Chapter 4: The Fourth Labor: The Erymanthian Boar 29 4.1 The Tasks 30 4.1.1 Exercise: The Centaurs' Wine 30 4.1.2 Chiron's Poison 30 4.1.3 The Capture of the Boar 31 4.2 The Solutions 31 4.2.1 Exercise: The Centaurs' Wine 32 4.2.2 Chiron's Poison 34 4.2.3 The Capture of the Boar 37 4.3 The Erymanthian Sudoku Puzzle 40 Chapter 5: The Fifth Labor: The Augean Stables 41 5.1 The Tasks 42 5.1.1 The Herds of Augeas 42 5.1.2 Exercise: Hydrostatic Pressure on the Stable Walls 43 5.1.3 Cleaning the Stables with Torricelli 43 5.2 The Solutions 43 5.2.1 The Herds of Augeas 43 5.2.2 Exercise: Hydrostatic Pressure on the Stable Walls 45 5.2.3 Cleaning the Stables with Torricelli 48 Chapter 6: The Sixth Labor: The Stymphalian Birds 53 6.1 The Tasks 53 6.1.1 The Spiral of Archimedes 54 6.1.2 Resonating Castanets 54 6.1.3 Exercise: Monte Carlo Shooting Scheme 55 6.2 The Solutions 55 6.2.1 The Spiral of Archimedes 55 6.2.2 Resonating Castanets 59 6.2.3 Exercise: A Monte Carlo Shooting Scheme 64 Chapter 7: The Seventh Labor: The Cretan Bull 69 7.1 The Tasks 69 7.1.1 Exercise: Riding the Bull 70 7.1.2 The Marathon Attacks 70 7.2 The Solutions 70 7.2.1 Exercise: Riding the Bull 70 7.2.2 The Marathon Attacks 73 Chapter 8: The Eighth Labor: The Horses of Diomedes 76 8.1 The Tasks 76 8.1.1 Driving the Mares to the Sea 77 8.1.2 Hercules' Slingshot 77 8.1.3 Exercise: The City of Abdera 78 8.2 The Solutions 78 8.2.1 Driving the Mares to the Sea 78 8.2.2 Hercules' Slingshot 81 8.2.3 Exercise: The City of Abdera 83 8.3 The Diomedes Sudoku Puzzle 87 Chapter 9: The Ninth Labor: The Belt of Hippolyte 89 9.1 The Tasks 90 9.1.1 The Sons of Minos versus Hercules 91 9.1.2 The Amazons and the Spread of a Rumor 91 9.1.3 Exercise: Hercules and the Kraken 92 9.2 The Solutions 92 9.2.1 The Sons of Minos versus Hercules 92 9.2.2 The Amazons and the Spread of a Rumor 98 9.2.3 Exercise: Hercules and the Kraken 101 Chapter 10: The Tenth Labor: Geryon's Cattle 104 10.1 The Tasks 105 10.1.1 The Pillars of Hercules 106 10.1.2 The Golden Goblet 106 10.1.3 Hera Sends the Gadflies 106 10.1.4 Blocking the River Strymon 107 10.2 The Solutions 107 10.2.1 The Pillars of Hercules 107 10.2.2 The Golden Goblet 110 10.2.3 Hera Sends the Gadflies 112 10.2.4 Blocking the River Strymon 114 Chapter 11: The Eleventh Labor: The Apples of the Hesperides 118 11.1 The Tasks 120 11.1.1 Exercise: The Riddles of Nereus 120 11.1.2 Wrestling Antaeus 121 11.1.3 Exercise: Hercules Has the Whole World in His Hands 121 11.2 The Solutions 122 11.2.1 Exercise: The Riddles of Nereus 122 11.2.2 Wrestling Antaeus 125 11.2.3 Exercise: Hercules Has the Whole World in His Hands 131 Chapter 12: The Twelfth Labor: Cerberus 134 12.1 The Tasks 135 12.1.1 The Descent into the Underworld 135 12.1.2 The Fight with Cerberus 135 12.2 The Solutions 136 12.2.1 The Descent into the Underworld 136 12.2.2 The Fight with Cerberus 139 12.3 The Cerberus Sudoku Puzzle 143 Appendix A: The Labors and Subject Areas of Mathematics 147 A.1 Subject Areas by Labors and Tasks 147 A.2 Tasks by Subject Area 149 Appendix B: Hercules before the Labors 151 B.1 Hercules' Background 151 Appendix C: The Authors of the Hercules Myth 154 C.1 The Authors 154 C.2 The Lay of the Labours of Hercules 156 Appendix D:The Laplace Transform 161 D.1 Initial Value Problems and the Laplace Transform 161 D.1.1 Theory 161 D.1.2 An Example 163 Appendix E: Solution to the Sudoku Puzzles 164 Bibliography 167 Index 171

"The figures and diagrams are well chosen, the mathematics is presented attractively, the pace is appropriate. Unobtrusively, the general level of mathematical sophistication tends to rise as the book progresses. This book offers ideas to teachers seeking topics on which to pin some abstract maths, and could encourage students to think imaginatively about their subject, and where it might arise in unexpected circumstances."--John Haigh, London Mathematical Society Newsletter "Though Mythematics is probably best viewed as a recreational mathematics book, the methods used should provide insight into how one applies mathematics to a physical, real-world problem. Students interested in mathematical modeling may certainly find this book of interest."--Choice "Never before has a Greek hero faced such trials armed first and foremost with the weapon of mathematics... This book is ideal for students, providing an entertaining way to practise problem-solving skills and a glimpse of how useful even basic mathematical ideas can be when applied to physical scenarios. The premise of Mythematics is both original and intriguing, but what is most impressive is Huber's inventiveness in translating the twelve labours of Hercules into mathematical conundrums."--Sarah Shepherd, iSquared "The book is unique in its mixture of ancient Greek mythology and applied mathematics... It will certainly be a valuable source of inspiration for math teachers who have to teach these students."--Adhemar Bultheel, European Mathematical Society