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Mythematics

Book Description

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.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. List of Figures
  6. Foreword
  7. Chapter 1 The First Labor: The Nemean Lion
    1. 1.1 The Tasks
      1. 1.1.1 Shooting an Arrow
      2. 1.1.2 Hercules Closes the Cave Mouth
      3. 1.1.3 Exercise: Zeus Makes a Deal
    2. 1.2 The Solutions
      1. 1.2.1 Shooting an Arrow
      2. 1.2.2 Hercules Closes the Cave Mouth
      3. 1.2.3 Exercise: Zeus Makes a Deal
  8. Chapter 2 The Second Labor: The Lernean Hydra
    1. 2.1 The Tasks
      1. 2.1.1 One Head Replaced by Two
      2. 2.1.2 Cauterizing the Hydra
    2. 2.2 The Solutions
      1. 2.2.1 One Head Replaced by Two
      2. 2.2.2 Cauterizing the Hydra
  9. Chapter 3 The Third Labor: The Hind of Ceryneia
    1. 3.1 The Tasks
      1. 3.1.1 Optimizing the Hind’s Journey
      2. 3.1.2 Cerynitian Work
      3. 3.1.3 Exercise: Work with a Variable Force
    2. 3.2 The Solutions
      1. 3.2.1 Optimizing the Hind’s Journey
      2. 3.2.2 Cerynitian Work
      3. 3.2.3 Exercise: Work with a Variable Force
  10. Chapter 4 The Fourth Labor: The Erymanthian Boar
    1. 4.1 The Tasks
      1. 4.1.1 Exercise: The Centaurs’ Wine
      2. 4.1.2 Chiron’s Poison
      3. 4.1.3 The Capture of the Boar
    2. 4.2 The Solutions
      1. 4.2.1 Exercise: The Centaurs’ Wine
      2. 4.2.2 Chiron’s Poison
      3. 4.2.3 The Capture of the Boar
    3. 4.3 The Erymanthian Sudoku Puzzle
  11. Chapter 5 The Fifth Labor: The Augean Stables
    1. 5.1 The Tasks
      1. 5.1.1 The Herds of Augeas
      2. 5.1.2 Exercise: Hydrostatic Pressure on the Stable Walls
      3. 5.1.3 Cleaning the Stables with Torricelli
    2. 5.2 The Solutions
      1. 5.2.1 The Herds of Augeas
      2. 5.2.2 Exercise: Hydrostatic Pressure on the Stable Walls
      3. 5.2.3 Cleaning the Stables with Torricelli
  12. Chapter 6 The Sixth Labor: The Stymphalian Birds
    1. 6.1 The Tasks
      1. 6.1.1 The Spiral of Archimedes
      2. 6.1.2 Resonating Castanets
      3. 6.1.3 Exercise: Monte Carlo Shooting Scheme
    2. 6.2 The Solutions
      1. 6.2.1 The Spiral of Archimedes
      2. 6.2.2 Resonating Castanets
      3. 6.2.3 Exercise: A Monte Carlo Shooting Scheme
  13. Chapter 7 The Seventh Labor: The Cretan Bull
    1. 7.1 The Tasks
      1. 7.1.1 Exercise: Riding the Bull
      2. 7.1.2 The Marathon Attacks
    2. 7.2 The Solutions
      1. 7.2.1 Exercise: Riding the Bull
      2. 7.2.2 The Marathon Attacks
  14. Chapter 8 The Eighth Labor: The Horses of Diomedes
    1. 8.1 The Tasks
      1. 8.1.1 Driving the Mares to the Sea
      2. 8.1.2 Hercules’ Slingshot
      3. 8.1.3 Exercise: The City of Abdera
    2. 8.2 The Solutions
      1. 8.2.1 Driving the Mares to the Sea
      2. 8.2.2 Hercules’ Slingshot
      3. 8.2.3 Exercise: The City of Abdera
    3. 8.3 The Diomedes Sudoku Puzzle
  15. Chapter 9 The Ninth Labor: The Belt of Hippolyte
    1. 9.1 The Tasks
      1. 9.1.1 The Sons of Minos versus Hercules
      2. 9.1.2 The Amazons and the Spread of a Rumor
      3. 9.1.3 Exercise: Hercules and the Kraken
    2. 9.2 The Solutions
      1. 9.2.1 The Sons of Minos versus Hercules
      2. 9.2.2 The Amazons and the Spread of a Rumor
      3. 9.2.3 Exercise: Hercules and the Kraken
  16. Chapter 10 The Tenth Labor: Geryon’s Cattle
    1. 10.1 The Tasks
      1. 10.1.1 The Pillars of Hercules
      2. 10.1.2 The Golden Goblet
      3. 10.1.3 Hera Sends the Gadflies
      4. 10.1.4 Blocking the River Strymon
    2. 10.2 The Solutions
      1. 10.2.1 The Pillars of Hercules
      2. 10.2.2 The Golden Goblet
      3. 10.2.3 Hera Sends the Gadflies
      4. 10.2.4 Blocking the River Strymon
  17. Chapter 11 The Eleventh Labor: The Apples of the Hesperides
    1. 11.1 The Tasks
      1. 11.1.1 Exercise: The Riddles of Nereus
      2. 11.1.2 Wrestling Antaeus
      3. 11.1.3 Exercise: Hercules Has the Whole World in His Hands
    2. 11.2 The Solutions
      1. 11.2.1 Exercise: The Riddles of Nereus
      2. 11.2.2 Wrestling Antaeus
      3. 11.2.3 Exercise: Hercules Has the Whole World in His Hands
  18. Chapter 12 The Twelfth Labor: Cerberus
    1. 12.1 The Tasks
      1. 12.1.1 The Descent into the Underworld
      2. 12.1.2 The Fight with Cerberus
    2. 12.2 The Solutions
      1. 12.2.1 The Descent into the Underworld
      2. 12.2.2 The Fight with Cerberus
    3. 12.3 The Cerberus Sudoku Puzzle
  19. Appendix A: The Labors and Subject Areas of Mathematics
    1. A.1 Subject Areas by Labors and Tasks
    2. A.2 Tasks by Subject Area
  20. Appendix B: Hercules before the Labors
    1. B.1 Hercules’ Background
  21. Appendix C: The Authors of the Hercules Myth
    1. C.1 The Authors
    2. C.2 The Lay of the Labours of Hercules
  22. Appendix D: The Laplace Transform
    1. D.1 Initial Value Problems and the Laplace Transform
    2. D.1.1 Theory
    3. D.1.2 An Example
  23. Appendix E: Solution to the Sudoku Puzzles
  24. Bibliography
  25. Index