Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression.

* Image sequence demonstrating Achilles tendinosis

The simulation, whose results were featured in the 2007 documentary Titanic ’ s Achilles Heel, partially refuted Long ’ s suspicions by demonstrating that Titanics expansion joints were strong enough to deal with any and all stresses the ship could reasonably be expected to encounter in service and, during the sinking, actually outperformed their design specifications.

* Image sequence demonstrating Achilles tendinosis and Achilles tendon rupture

Three of the strongest and most famous — that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight — are presented in detail below.

The tortoise discusses with Achilles a simple deductive argument.

In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument.

The Tortoise then asks Achilles whether there might be a reader of Euclid who grants that the argument is logically valid, as a sequence, while denying that A and B are true.

The Tortoise agrees to accept C, if Achilles will write down what it has to accept in his notebook, making the new argument:

The argument attempts to show that even though Achilles runs faster than the Tortoise, he will never catch up with her because, when Achilles reaches the point at which the Tortoise started, the Tortoise has advanced some distance beyond ; when Achilles arrives at the point where the Tortoise was when Achilles arrived at the point where the Tortoise started, the Tortoise has again moved forward.

As he died because of a small wound on his heel, the term Achilles ' heel has come to mean one's point of weakness.

Achilles was absent during these encounters because of his feud with Agamemnon.

They quickly became the Achilles ' heel of the system because of their combination of an overly complex mechanical design with a very low-cost internal flex circuit system.

The goddesses Hera, Athena and Aphrodite had been invited along with the rest of Olympus to the forced wedding of Peleus and Thetis, who would become the parents of Achilles, but Eris had been snubbed because of her troublemaking inclinations.

Hector chooses to remain outside the gates of Troy and face Achilles, partially because had he listened to Polydamas and retreated with his troops the previous night, Achilles would not have killed so many Trojans.

It is slightly contradictory because Larissa was also the birthplace of Achilles sworn enemy of Troyans.

They ( by usual tradition Neoptolemus ) also sacrificed the Trojan princess Polyxena on the grave of Achilles as demanded by his ghost, either as part of his spoil or because she had betrayed him.

Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

He received the nickname Achilles because of his knightly qualities.

He says that even if Achilles somehow manages to leave Troy, he will never be able to stay away from battle because he cannot change the fate ; " let him go or stay — the gods will make sure that he will fight.

The embassy failed because Achilles himself had more faith in his own choices than fate or divine interventions.

Thersites mocked Achilles for his behaviour, because the hero was mourning his enemy.

In his Introduction to The Anger of Achilles, Robert Graves speculates that Homer might have made Thersites a ridiculous figure as a way of dissociating himself from him, because his remarks seem entirely justified.

Accepting a tip from inside China, where Achilles is held prisoner, Peter had planned for Bean to operate the mission, but at the last minute ( because he doubted Bean would cooperate ) assigns Suriyawong, a battle school student from Thailand, to rescue Achilles in transport, believing that he can spy on Achilles, take over his network, and then turn Achilles over to some country for trial ( at the time of this story, Achilles has betrayed Russia, Pakistan, and India ).

In 2005 a fight with Lucia Rijker, entitled " Million Dollar Lady ", was canceled because Rijker ruptured her Achilles during training.

Achilles and his Myrmidons do not fight the next day because of Agamemnon's unfair claim to Briseis.

Dokic then received a qualification wildcard into the Moorilla Hobart International tournament but withdrew before her first match because of an Achilles tendon injury.

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise.

Achilles allows the tortoise a head start of 100 metres, for example.

It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther ; and then more time still to reach this third point, while the tortoise moves ahead.

Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go.

Expressed this way, the dichotomy paradox is very much analogous to that of Achilles and the tortoise.

* Leo Tolstoy in War and Peace ( Part 11, Chapter I ) discusses the race of Achilles and the tortoise when critiquing " historical science ".

* In Gödel, Escher, Bach by Douglas Hofstadter, the various chapters are separated by dialogues between Achilles and the tortoise, inspired by Lewis Carroll ’ s works.

The main chapters alternate with dialogues between imaginary characters, usually Achilles and the tortoise, first used by Zeno of Elea and later by Lewis Carroll in " What the Tortoise Said to Achilles ".

The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race.

The human comedy is interspersed by descriptions of the animal life which Gerald observes on his expeditions around the family homes, island, and seashore and which he frequently brings back and keeps as pets ; these include Achilles the tortoise, Quasimodo the pigeon, Ulysses the Scops owl, numerous spiders, Alecko the gull, puppies named Widdle and Puke, and the birds known as the Magenpies.

The naming of tortoise coordinate comes from one of Zeno of Elea's paradoxes on an imaginary footrace between " swift-footed " Achilles and a tortoise.

Zeno himself also discusses the notion of what he calls " Achilles and the tortoise ".

Achilles chases a tortoise, an animal renowned for being slow, that moves at 0. 1 m / s.

Common sense seems to decree that Achilles will catch up with the tortoise after exactly 1 second, but Zeno argues that this is not the case.