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It is sometimes difficult to determine which ideas Pythagoras taught originally, as opposed to the ideas his followers later added. While he clearly attached great importance to geometry, classical Greek writers tended to cite Thales as the great pioneer of this science rather than Pythagoras. The later tradition of Pythagoras as the inventor of mathematics stems largely from the Roman period.

The shores of the Aegean Sea saw the emergence of the first civilizations in Europe, namely the Minoan and Mycenaean civilisations. After these subsided a Dark Age followed until around 800 BC a new era of Greek civilization emerged. This Greece of city-states established colonies along the Mediterranean and partially resisted Persian invasions. Greek culture would later become the basis of the Hellenistic civilisation that followed the empire of Macedonian King Alexander of Macedon.

Whether or not we attribute the Pythagorean theorem to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean tradition and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school -- which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties -- was the incommensurability of the diagonal of a square with its side. This result showed the existence of irrational numbers.

Architecture (building executed to an aesthetically considered design) was extinct in Greece from the end of the Mycenaean period (about 1200 BC) until the 7th century, when urban life and prosperity recovered to a point where public building could be undertaken. But since most Greek buildings in the Archaic and Early Classical periods were made of wood or mud-brick, nothing remains of them except a few ground-plans, and there are almost no written sources on early architecture or descriptions of buildings. Most of our knowledge of Greek architecture comes from the few surviving buildings of the Classical, Hellenistic and Roman periods (since Roman architecture heavily copied Greek), and from late written sources such as Vitruvius (1st century AD). This means that there is a strong bias towards temples, the only buildings which survive in any number.

Votives were kept on display in the god's sanctuary for a set period of time and then were usually ritually discarded. Bronze tripods, prize cauldrons and figurines, terracotta tablets and figurines, lamps, and vases are typical examples. Armor, weapons, jewelry and other more personalized items were dedicated in large numbers, along with marble statuettes and reliefs. Some of the healing sanctuaries housed replicas of body parts donated in thanks for or in hope of cures. Large sculptural monuments in bronze, marble and other costly materials were routinely dedicated by either private donors or individual city-states in the great Panhellenic sanctuaries like Olympia and Delphi.

Thales lived in the city of Miletus, in Ionia. According to Herodotus, he was of Phoenician descent. The well-traveled Ionians had many dealings with Egypt and Babylon, and Thales may have studied in Egypt as a young man. In any event, Thales almost certainly had exposure to Egyptian mythology, astronomy, and mathematics, as well as to other traditions alien to the Homeric traditions of Greece. Perhaps because of this his inquiries into the nature of things took him beyond traditional mythology.

The oldest surviving folk songs in all of Greece can be traced to the 17th century, when songs in the rizitika type were recorded by monks at Iviron and Xyropotamos at Mount Athos. Recording secular folk songs was almost certainly forbidden by the monk's code of conduct. However, the connection between music and religion continues in modern Crete; priests are said to be excellent folk singers, including the rizitiko singer Aggelos Psilakis. It was during this period, when modern Cretan folk music was formed, that Francisco Leontaritis was active. Leontaritis is said to be the father of modern Greek music.

An overview of the 2004 Olympic infrastructureDespite the country's numerically small and ill-equipped armed forces, Greece made a decisive contribution to the Allied efforts in World War II. At the start of the war Greece sided with the Allies and refused to give in to Italian demands. Italy invaded Greece on 28 October 1940, but Greek troops repelled the invaders after a bitter struggle. This marked the first Allied victory in the war. Hitler then reluctantly stepped in, primarily to secure his strategic southern flank: troops from Germany, Hungary, Bulgaria and Italy successfully invaded Greece, overcoming Greek, British, Australian and New Zealand units.

Art historians generally define Ancient Greek art as the art produced in the Greek-speaking world from about 1000 BC to about 100 BC. They generally exclude the art of the Mycenaean and Minoan civilisations, which flourished from about 1500 to about 1200 BC. Despite the fact that these were Greek-speaking cultures, there is little or no continuity between the art of these civilisations and later Greek art.

Tourism is a major source of foreign exchange earnings. Although it is one of the country's most important industries, it has been slow to expand and suffers from poor infrastructure. With more than 14 million tourists visiting Greece in 2002, the tourist industry faced declining revenues, partly due to the strong drachma. Revenue from tourism exceeded $5.2 billion in 1998, having increased somewhat as Greek tourism benefited from problems in neighboring countries and an economic recovery in the European Union.

In addition to the local cults of major gods, various places like crossroads and sacred groves had their own tutelary spirits. There were often altars erected outside the precincts of the temples. Shrines like hermai were erected outside the temples as well. Heroes, in the original sense, were demigods or deified humans who were part of local legendary history; they too had local hero-cults, and often served as oracles for purposes of divination. What religion was, first and foremost, was traditional; the idea of novelty or innovation in worship was out of the question, almost by definition. Religion was the collection of local practices to honour the local gods.

The Muslim minority, concentrated in Thrace, was given legal status by provisions of the Treaty of Lausanne in 1923 and is Greece's only officially recognized religious minority.

He never defined this principle precisely, and it has generally (e.g. by Aristotle and Augustine) been understood as a sort of primal chaos. It embraced the opposites of hot and cold, wet and dry, and directed the movement of things, by which there grew up all of the host of shapes and differences which are found in the world.

Greece is located in southeastern Europe on the southern tip of the Balkan peninsula. The Greek mainland is bounded on the north by Bulgaria, the Former Yugoslav Republic of Macedonia, and Albania; on the east by the Aegean Sea and Turkey; and on the west and south by the Ionian and Mediterranean Seas. The country consists of a large mainland; the Peloponnesos, a peninsula connected to the mainland by the Isthmus of Corinth; and more than 1,400 islands, including Crete, Rhodes, Corfu, and the Dodecanese and Cycladic groups. Greece has more than 14,880 kilometers (9,300 mi.) of coastline and a land boundary of 1,160 kilometers (726 mi.).