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Mythematics: Solving the Twelve Labors of Hercules

Michael Huber
Copyright Date: 2009
Pages: 216
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  • Book Info
    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,Mythematicsshows 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.Mythematicsprovides 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,Mythematicswill enlighten and delight mathematics and classics enthusiasts alike.

    eISBN: 978-1-4008-3190-6
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-xii)
    (pp. xiii-xiv)
    (pp. xv-xxii)
    Michael Huber

    Hercules (or, Herakles, as he was known to Greeks) is a hero well known for his strength and ingenuity. According toThe Oxford Classical Dictionary, he shared the characteristics of, on the one hand, a hero (both cultic and epic) and, on the other hand, a god. He is arguably the greatest and most famous of the classical Greek heroes. The mythology surrounding Hercules has been a part of human culture for over 2500 years. Many students get a glimpse of Hercules long before they go to high school or college. Whether it is from a civilizations history course, a...

  5. CHAPTER 1 The First Labor: The Nemean Lion
    (pp. 1-12)

    First, Eurystheus ordered him to bring the skin of the Nemean lion; now that was an invulnerable beast begotten by Typhon. On his way to attack the lion he came to Cleonae and lodged at the house of a day-laborer, Molorchus; and when his host would have offered a victim in sacrifice, Hercules told him to wait for thirty days, and then, if he had returned safe from the hunt, to sacrifice to Saviour Zeus, but if he were dead, to sacrifice to him as to a hero. And having come to Nemea and tracked the lion, he first shot...

  6. CHAPTER 2 The Second Labor: The Lernean Hydra
    (pp. 13-19)

    As a second labour he [Eurystheus] ordered him to kill the Lernean hydra. That creature, bred in the swamp of Lerna, used to go forth into the plain and ravage both the cattle and the country. Now the hydra had a huge body, with nine heads, eight mortal, but the middle one immortal. So mounting a chariot driven by Iolaus, he came to Lerna, and having halted his horses, he discovered the hydra on a hill beside the springs of the Amymone, where was its den. By pelting it with fiery shafts he forced it to come out, and in...

  7. CHAPTER 3 The Third Labor: The Hind of Ceryneia
    (pp. 20-28)

    From Apollodorus:

    As a third labour he ordered him to bring the Cerynitian hind alive to Mycenae. Now the hind was at Oenoe; it had golden horns and was sacred to Artemis; so wishing neither to kill nor wound it, Hercules hunted it a whole year. But when, weary with the chase, the beast took refuge on the mountain called Artemisius, and thence passed to the river Ladon, Hercules shot it just as it was about to cross the stream, and catching it put it on his shoulders and hastened through Arcadia. But Artemis with Apollo met him, and would...

  8. CHAPTER 4 The Fourth Labor: The Erymanthian Boar
    (pp. 29-40)

    As a fourth labour he ordered him to bring the Erymanthian boar alive; now that animal ravaged Psophis, sallying from a mountain which they call Erymanthus. So passing through Pholoe he was entertained by the centaur Pholus, a son of Silenus by a Melian nymph. He set roast meat before Hercules, while he himself ate his meat raw. When Hercules called for wine, he said he feared to open the jar which belonged to the centaurs in common. But Hercules, bidding him be of good courage, opened it, and not long afterwards, scenting the smell, the centaurs arrived at the...

  9. CHATPER 5 The Fifth Labor: The Augean Stables
    (pp. 41-52)

    From Apollodorus:

    The fifth labour he laid on him was to carry out the dung of the cattle of Augeas in a single day. Now Augeas was king of Elis; some say that he was a son of the Sun, others that he was a son of Poseidon, and others that he was a son of Phorbas; and he had many herds of cattle. Hercules accosted him, and without revealing the command of Eurystheus, said that he would carry out the dung in one day, if Augeas would give him the tithe of the cattle. Augeas was incredulous, but promised....

  10. CHAPTER 6 The Sixth Labor: The Stymphalian Birds
    (pp. 53-68)

    From Apollodorus:

    The sixth labour he enjoined on him was to chase away the Stymphalian birds. Now at the city of Stymphalus in Arcadia was the lake called Stymphalian, embosomed in a deep wood. To it countless birds had flocked for refuge, fearing to be preyed upon by the wolves. So when Hercules was at a loss how to drive the birds from the wood, Athena gave him brazen castanets, which she had received from Hephaestus. By clashing these on a certain mountain that overhung the lake, he scared the birds. They could not abide the sound, but fluttered up...

  11. CHAPTER 7 The Seventh Labor: The Cretan Bull
    (pp. 69-75)

    From Apollodorus:

    The seventh labour he enjoined on him was to bring the Cretan bull. Acusilaus says that this was the bull that ferried across Europa for Zeus; but some say it was the bull that Poseidon sent up from the sea when Minos promised to sacrifice to Poseidon what should appear out of the sea. And they say that when he saw the beauty of the bull he sent it away to the herds and sacrificed another to Poseidon; at which the god was angry and made the bull savage. To attack this bull Hercules came to Crete, and...

  12. CHAPTER 8 The Eighth Labor: The Horses of Diomedes
    (pp. 76-88)

    From Apollodorus:

    The eighth labour he enjoined on him was to bring the mares of Diomedes the Thracian to Mycenae. Now this Diomedes was a son of Ares and Cyrene, and he was king of the Bistones, a very warlike Thracian people, and he owned man-eating mares. So Hercules sailed with a band of volunteers, and having overpowered the grooms who were in charge of the mangers, he drove the mares to the sea. When the Bistones in arms came to the rescue, he committed the mares to the guardianship of Abderus, who was a son of Hermes, a native...

  13. CHAPTER 9 The Ninth Labor: The Belt of Hippolyte
    (pp. 89-103)

    From Apollodorus:

    The ninth labour he enjoined on Hercules was to bring the belt of Hippolyte. She was queen of the Amazons, who dwelt about the river Thermodon, a people great in war; for they cultivated the manly virtues, and if ever they gave birth to children through intercourse with the other sex, they reared the females; and they pinched off the right breasts that they might not be trammelled by them in throwing the javelin, but they kept the left breasts, that they might suckle. Now Hippolyte had the belt of Ares in token of her superiority to all...

  14. CHAPTER 10 The Tenth Labor: Geryon’s Cattle
    (pp. 104-117)

    From Apollodorus:

    As a tenth labour he was ordered to fetch the kine of Geryon from Erythia. Now Erythia was an island near the ocean; it is now called Gadira. This island was inhabited by Geryon, son of Chrysaor by Callirrhoe, daughter of Ocean. He had the body of three men grown together and joined in one at the waist, but parted in three from the flanks and thighs. He owned red kine, of which Eurytion was the herdsman and Orthus, the two-headed hound, begotten by Typhon on Echidna, was the watchdog. So journeying through Europe to fetch the kine...

  15. CHAPTER 11 The Eleventh Labor: The Apples of the Hesperides
    (pp. 118-133)

    From Apollodorus:

    When the labours had been performed in eight years and a month, Eurystheus ordered Hercules, as an eleventh labour, to fetch golden apples from the Hesperides, for he did not acknowledge the labour of the cattle of Augeas nor that of the hydra. These apples were not, as some have said, in Libya, but on Atlas among the Hyperboreans. They were presented by Earth to Zeus after his marriage with Hera, and guarded by an immortal dragon with a hundred heads, offspring of Typhon and Echidna, which spoke with many and divers sorts of voices. With it the...

  16. CHAPTER 12 The Twelfth Labor: Cerberus
    (pp. 134-144)

    From Apollodorus:

    A twelfth labour imposed on Hercules was to bring Cerberus from Hades. Now this Cerberus had three heads of dogs, the tail of a dragon, and on his back the heads of all sorts of snakes. When Hercules was about to depart to fetch him, he went to Eumolpus at Eleusis, wishing to be initiated. However it was not then lawful for foreigners to be initiated: since he proposed to be initiated as the adoptive son of Pylius. But not being able to see the mysteries because he had not been cleansed of the slaughter of the centaurs,...

  17. Appendix A: The Labors and Subject Areas of Mathematics
    (pp. 147-150)
  18. Appendix B: Hercules before the Labors
    (pp. 151-153)
  19. Appendix C: The Authors of the Hercules Myth
    (pp. 154-160)
  20. Appendix D: The Laplace Transform
    (pp. 161-163)
  21. Appendix E: Solution to the Sudoku Puzzles
    (pp. 164-166)
    (pp. 167-170)
  23. INDEX
    (pp. 171-183)