Synopses & Reviews
How might Hercules, the most famous of the Greek heroes, have used mathematics to complete his astonishing Twelve Labors? From conquering the Nemean Lion and cleaning out the Augean Stables, to capturing the Erymanthean Boar and entering the Underworld to defeat the three-headed dog Cerberus, Hercules and his legend are the inspiration for this book of fun and original math puzzles.
While Hercules relied on superhuman strength to accomplish the Twelve Labors, Mythematics shows how math could have helped during his quest. How does Hercules defeat the Lernean Hydra and stop its heads from multiplying? Can Hercules clean the Augean Stables in a day? What is the probability that the Cretan Bull will attack the citizens of Marathon? How does Hercules deal with the terrifying Kraken? Michael Huber's inventive math problems are accompanied by short descriptions of the Twelve Labors, taken from the writings of Apollodorus, who chronicled the life of Hercules two thousand years ago. Tasks are approached from a mathematical modeling viewpoint, requiring varying levels of knowledge, from basic logic and geometry to differential and integral calculus. Mythematics provides helpful hints and complete solutions, and the appendixes include a brief history of the Hercules tale, a review of mathematics and equations, and a guide to the various disciplines of math used throughout the book.
An engaging combination of ancient mythology and modern mathematics, Mythematics will enlighten and delight mathematics and classics enthusiasts alike.
Review
"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
Review
"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
Review
"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
Review
"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
Synopsis
"In this one-of-a-kind book, Michael Huber converts the Twelve Labors of Hercules into a series of math problems, thereby demonstrating the chops of an applied mathematician and the sensibility of a classicist. We can only hope that, for a sequel, Huber takes on
A Thousand and One Nights."
--William Dunham, author of The Calculus Gallery"Huber has come up with a clever means to present some pretty mathematics and math modeling. Covering an eclectic set of topics, this book will teach readers a golden goblet's worth of mathematics."--Colin Adams, coauthor of How to Ace Calculus
"Michael Huber ingeniously introduces many elementary mathematical and physical problems in this fascinating book. Who knew Greek mythology could be so mathematical!"--John Adam, coauthor of Guesstimation
"This book does an excellent job of blending math with a very different field--classics. As I read the book I thought, 'Had one of the gods offered Hercules a premonition of this book's contents, he would have quickly trained to have strength in mathematical insights to rival his physical prowess.' The book repeatedly underscores the importance of careful mathematical modeling."--Tim Chartier, Davidson College
"I like the concepts underlying the problems in this book. It will be a valuable resource for classroom teachers at all levels and a fun read for students."--John Quintanilla, University of North Texas
About the Author
Michael Huber is associate professor of mathematics at Muhlenberg College.
Table of Contents
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