Ancient Greece

Athenian democracy developed around the 6th century BC in the Greek city-state (known as a polis) of Athens, comprising the city of Athens and the surrounding territory of Attica, and focusing on supporting liberty, equality, and security. Although Athens is the most familiar of the democratic city-states in ancient Greece, it was not the only one, nor was it the first; multiple other city-states adopted similar democratic constitutions before Athens. By the late 4th century BC, as many as half of the over one thousand existing Greek cities might have been democracies. Athens practiced a political system of legislation and executive bills. Participation was open to adult, free male citizens (i.e., not a metic, woman or slave). Adult male citizens probably constituted no more than 30 percent of the total adult population.

Solon (in 594 BC), Cleisthenes (in 508–07 BC), and Ephialtes (in 462 BC) contributed to the development of Athenian democracy. Cleisthenes broke up the unlimited power of the nobility by organizing citizens into ten groups based on where they lived, rather than on their wealth. The longest-lasting democratic leader was Pericles. After his death, Athenian democracy was twice briefly interrupted by oligarchic revolutions in 411 and 404 BC, towards the end of the Peloponnesian War. It was modified somewhat after it was restored under Eucleides; the most detailed accounts of the system are of this fourth-century modification, rather than the Periclean system. Democracy was suppressed by the Macedonians in 322 BC. The Athenian institutions were later revived, but how close they were to the original forms of democracy is debated.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

Philip II of Macedon (Ancient Greek: Φίλιππος, romanized: Phílippos; 382 BC – October 336 BC) was the king (basileus) of Macedon from 359 BC until his death in 336 BC. The rise of Macedon, from a kingdom initially at the periphery of classical Greek affairs, to a power that came to dominate Ancient Greece in the span of less than 25 years, was largely thanks to the character and policies of Philip. He was the father of Alexander the Great and a member of the ruling Argead dynasty that founded the kingdom of the Macedonians.

Philip achieved to dominate Greece during his reign by the reformation of the Macedonian army, including the establishment of the Macedonian phalanx, the use of combined arms tactics and his extensive use of siege engines and artillery, as well as by the use of effective diplomacy and marriage alliances. After defeating the Greek city-states of Athens and Thebes at the Battle of Chaeronea in 338 BC, Philip II led the effort to establish a federation of Greek states known as the Hellenic League, with him as the elected hegemon and commander-in-chief of Greece for a planned invasion of the Achaemenid Empire. However, his assassination by a royal bodyguard, Pausanias of Orestis, led to the immediate succession of his son Alexander, who would go on to invade the Achaemenid Empire in his father's stead.

The League of Corinth, also referred to as the Hellenic League (Greek: κοινὸν τῶν Ἑλλήνων, koinòn tõn Hellḗnōn; or simply οἱ Ἕλληνες, the Héllēnes), was a federation of Greek states created by Philip II in 338–337 BC. The League was created in order to unify Greek military forces under Macedonian leadership (hegemony) in their combined conquest of the Persian Achaemenid Empire.

King Philip was initially urged by Isocrates in 346 BC to unify Greece against the Persians. After the Battle of Chaeronea, the League of Corinth was formed and controlled by Philip. Alexander utilized his father's league when planning his pan-Hellenic invasion of Asia to expand Macedon and take revenge on the Persian Empire. During the Hellenistic period, some Antigonid rulers of Macedon shortly revived the league, also known as the 'Hellenic Alliance'.

Alexander III of Macedon (Ancient Greek: Ἀλέξανδρος, romanized: Aléxandros; 20/21 July 356 BC – 10/11 June 323 BC), most commonly known as Alexander the Great, was king of the ancient Greek kingdom of Macedon. He succeeded his father Philip II to the throne in 336 BC at the age of 20, and spent most of his regency conducting a lengthy military campaign throughout parts of Asia and Egypt. By the age of 30, he had created one of the largest empires in history, stretching from Greece to northwestern India. He was undefeated in battle and is widely considered to be one of history's greatest and most successful military commanders.

Alexander was tutored by Aristotle until the age of 16. In 335 BC, shortly after assuming the throne of Macedon, he launched a campaign in the Balkans and reasserted control over Thrace and parts of Illyria before marching on the city of Thebes, which was subsequently destroyed in battle. Alexander then assumed leadership of the League of Corinth, created by his father, and with his authority over all Greeks he launched a pan-Hellenic campaign to invade the Persia.

The culture of Greece has evolved over thousands of years, beginning in Minoan and later in Mycenaean Greece, continuing most notably into Classical Greece, while influencing the Roman Empire and its successor the Byzantine Empire. Other cultures and states such as the Frankish states, the Ottoman Empire, the Venetian Republic and Bavarian and Danish monarchies have also left their influence on modern Greek culture. Also they believed in greek mythology

Modern democracies owe a debt to Greek beliefs in government by the people, trial by jury, and equality under the law. The ancient Greeks pioneered in many fields that rely on systematic thought, including biology, geometry, history, philosophy, and physics. They introduced important literary forms as epic and lyric poetry, history, tragedy, and comedy. In their pursuit of order and proportion, the Greeks created an ideal of beauty that strongly influenced Western art.

The Roman Republic (Latin: Res publica Romana [ˈreːs ˈpuːblɪka roːˈmaːna]) was the era of classical Roman civilisation beginning with the overthrow of the Roman Kingdom (traditionally dated to 509 BC) and ending in 27 BC with the establishment of the Roman Empire following the War of Actium. During this period, Rome's control expanded from the city's immediate surroundings to hegemony over the entire Mediterranean world.

Roman society at the time was primarily a cultural mix of Latin and Etruscan societies, as well as of Sabine, Oscan, and Greek cultural elements, which is especially visible in the ancient Roman religion and its pantheon. Its political organisation developed at around the same time as direct democracy in ancient Greece, with collective and annual magistracies, overseen by a senate. There were annual elections, but the republican system was an elective oligarchy, not a democracy, with a number of powerful families largely monopolising the senior magistracies. Roman institutions underwent considerable changes throughout the Republic to adapt to difficulties such as the creation of promagistracies to rule its conquered provinces and, after the Social War during the late Republic, the inclusion of peninsular Italians as citizens and senators.

Religious practices in ancient Greece encompassed a collection of beliefs, rituals, and mythology, in the form of both popular public religion and cult practices. The application of the modern concept of "religion" to ancient cultures has been questioned as anachronistic. The ancient Greeks did not have a word for 'religion' in the modern sense. Likewise, no Greek writer is known to have classified either the gods or the cult practices into separate 'religions'. Instead, for example, Herodotus speaks of the Hellenes as having "common shrines of the gods and sacrifices, and the same kinds of customs".

Most ancient Greeks recognized the twelve major Olympian gods and goddesses—Zeus, Hera, Poseidon, Demeter, Athena, Ares, Aphrodite, Apollo, Artemis, Hephaestus, Hermes, and either Hestia or Dionysus—although philosophies such as Stoicism and some forms of Platonism used language that seems to assume a single transcendent deity. The worship of these deities, and several others, was found across the Greek world, though they often have different epithets that distinguished aspects of the deity, and often reflect the absorption of other local deities into the pan-Hellenic scheme.

In ancient Greece, deities were regarded as immortal, anthropomorphic, and powerful. They were conceived of as individual persons, rather than abstract concepts or notions, and were described as being similar to humans in appearance, albeit larger and more beautiful. The emotions and actions of deities were largely the same as those of humans; they frequently engaged in sexual activity, and were jealous and amoral. Deities were considered far more knowledgeable than humans, and it was believed that they conversed in a language of their own. Their immortality, the defining marker of their godhood, meant that they ceased aging after growing to a certain point. In place of blood, their veins flowed with ichor, a substance which was a product of their diet, and conferred upon them their immortality. Divine power allowed the gods to intervene in mortal affairs in various ways: they could cause natural events such as rain, wind, the growing of crops, or epidemics, and were able to dictate the outcomes of complex human events, such as battles or political situations.

As ancient Greek religion was polytheistic, a multiplicity of gods were venerated by the same groups and individuals. The identity of a deity was demarcated primarily by their name, which could be accompanied by an epithet (a title or surname); religious epithets could refer to specific functions of a god, to connections with other deities, or to a divinity's local forms. The Greeks honoured the gods by means of worship, as they believed deities were capable of bringing to their lives positive outcomes outside their own control. Greek cult, or religious practice, consisted of activities such sacrifices, prayers, libations, festivals, and the building of temples. By the 8th century BC, most deities were honoured in sanctuaries (temenē), sacred areas which often included a temple and dining room, and were typically dedicated to a single deity. Aspects of a god's cult such as the kinds of sacrifices made to them and the placement of their sanctuaries contributed to the distinct conception worshippers had of them.

Mycenaean Greece (or the Mycenaean civilization) was the last phase of the Bronze Age in ancient Greece, spanning the period from approximately 1750 to 1050 BC. It represents the first advanced and distinctively Greek civilization in mainland Greece with its palatial states, urban organization, works of art, and writing system. The Mycenaeans were mainland Greek peoples who were likely stimulated by their contact with insular Minoan Crete and other Mediterranean cultures to develop a more sophisticated sociopolitical culture of their own. The most prominent site was Mycenae, after which the culture of this era is named. Other centers of power that emerged included Pylos, Tiryns, and Midea in the Peloponnese, Orchomenos, Thebes, and Athens in Central Greece, and Iolcos in Thessaly. Mycenaean settlements also appeared in Epirus, Macedonia, on islands in the Aegean Sea, on the south-west coast of Asia Minor, and on Cyprus, while Mycenaean-influenced settlements appeared in the Levant and Italy.

The Mycenaean Greeks introduced several innovations in the fields of engineering, architecture and military infrastructure, while trade over vast areas of the Mediterranean was essential for the Mycenaean economy. Their syllabic script, Linear B, offers the first written records of the Greek language, and their religion already included several deities also to be found in the Olympic pantheon. Mycenaean Greece was dominated by a warrior elite society and consisted of a network of palace-centered states that developed rigid hierarchical, political, social, and economic systems. At the head of this society was the king, known as a wanax.