Sparta was a prominent city-state in the classical period, however it was ruled by a king, so they did not practice democracy. Macedon was a more traditional kingdom in mainland Greece - not a city-state at all - so that would not be a good choice for this question. Corinth and Argos were city-states but they did not invent democracy, so they would not be the best answer here. Finally, Athens is famous for inventing and practicing democracy, so that would be the best choice here.

Plato, while an ancient Greek philosopher of great renown, did not invent the dialectic method, so he would not be the best choice. Aristotle, too, was a prominent Greek philosopher but did not invent the method in question, so he also would not be the best choice. Rene Descartes was a French philosopher and lived many centuries after the time period on question, so he would not be a good answer. Bertrand Russel was a late 19th and early 20th century mathematician and philosopher and he did not invent the method in question, so he would not be the best choice. Finally Socrates, who famously invented the dialectic method, would be the best answer to this question.

Epicurus was an ancient Greek philosopher but he did not attend the Academy nor did he invent the syllogism, so he would not be the best choice. Marcus Aurelius was a Roman emperor and Stoic and he did not do either of the acts in question, so he too would not be the best choice. John Locke was an English philosopher that lived many centuries after the Academy, so he would not be a good answer here. And Thomas Hobbes similarly lived many centuries after the Academy, and so he also is not a good choice. Lastly, Aristotle both attended the Academy and developed the syllogism, so he would be the best answer to the question.

Homer was the epic poet who wrote The Odyssey and The Iliad, but he was not known for his accounts of history, so he would not be the best choice. Plato and Aristotle were philosophers of great renown but neither were concerned with historical accounts, so neither of them would be good choices. Epicurus was concerned with philosophy and the problem of evil, so he too would not be a good choice. Lastly, Herodotus is famous for his account of the Peloponnesian War and he was named the father of history by Cicero, so he would be the best answer.

Archimedes was a philosopher and mathematician; however, he is best known for discovering buoyancy, so he would not be the best choice. Plato and Aristotle were both ancient Greek philosophers, but they are best known for their work regarding the World of Forms and natural philosophy, respectively, so neither of them would be the best choice. Socrates pioneered the dialectic method and had some thoughts about living the good life, but he was not known for an interest in the problem of evil, so he would not be the best answer here. Lastly, Epicurus was concerned both with the good life and the problem of evil, so he would be the best choice here.

Archimedes was a mathematician and philosopher, however he was most famous for his discovery of buoyancy, so he would not be the best answer. Plato and Aristotle were philosophers but did not write extensively regarding mathematics, so they would not be good answers here. Socrates was also a philosopher and not a mathematician, so he would not be a good answer. Euclid wrote Elements -the premiere geometry textbook for millennia- and normal geometry is named after him, so he would be the best choice.

While Athenian culture exuded some of the other features, competition was a hallmark of Athens. This is evident from depictions of the Olympic games and many other frequent small sporting events found on Greek pottery and architecture. 

The Ancient Greek word polis refers to the large city-states of Greece.

Athens formed the Delian League with surrounding Greek city-states in order to better coordinate defense against external forces (such as the Persians). The other answers are incorrect because they contain terms not relevant to this part of Ancient Greek history.

The two "superpowers" of Greece, Athens and Sparta, warred against each other in the Peloponnesian Wars during the mid-fifth century BCE. The war resulted in a temporary supremacy of the Spartans in Greece. The other answers are incorrect because they refer to other nearby factions not involved in the conflict.