Mythematics: Solving the 12 Labors of Hercules

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