1. A short history of ancient Greece

2. We are now in 1000-500 BC …

4. The Minoans were a pre- Hellenic Bronze Age civilization in the island of Crete, the large island South of mainland Greece. Their civilization flourished from approximately 2600 to 1450 BC. Their culture, from ca 1700 BC onwards, shows a high degree of organization.

5. Around 1650 BC, 1500 BC, or 1450 BC (still debated), the volcanic island Thera at about 50 miles distance from Crete, erupted. The volcanic eruption and fallout was quite large. The massive eruption of Thera also led to the volcano's collapse, causing a massive Tsunami which destroyed naval installations and settlements near the coasts. The Minoan empire never recovered from that natural disaster and soon after the Tsunami the colonies in mainland Greece rebelled to the Minoans and took over.

6. The next successful civilization in Greece was that of Mycenae, by the name of a city located slightly to the southwest of Corinth. Mycenae reached the height of its power between 1400 and 1200 B.C. Elaborate ornaments and artwork attest to the Mycenaean civilization's vast wealth.

7. Their cities were ruled by strong palace- centered kings, and each city appears to have enjoyed a considerable autonomy. According to Homer's Iliad, the Mycenaean cities were united in a brief war against the City of Troy, a wealthy outpost on the west coast of Asia Minor (modern Turkey, see above map). But Homer's Iliad is a poem, not an historical source. Certainly, many of the stories that appear in the famous Iliad and Odyssey epics (written between 725 and 675 B.C) were legends originally passed from one generation to another orally.

8. Whether there was actually a beautiful princess, Helen of Troy ("the face that launched a thousand ships"), or a Trojan Horse is debatable. I It’s debatable whether there was actually a Trojan horse or a beautiful princess Helena who instigated the war…

9. Mycenaean civilization went into decline during the 13th century, B.C. For one thing, piracy throughout the Mediterranean diminished Mycenaean commerce. People who spoke a dialect of Greek known as Doric began to overrun Mycenae; these Dorian invasions, combined with internal conflicts among Mycenaean kings, doubtless contributed to the decline of the civilization. But, as with the demise of Crete, no one is entirely sure of what caused the final decline of this Bronze Age society.

10. The "Dark Ages" of Greece With the decline of Mycenaean civilization, Greece entered a sort of "Dark Ages." The archaeological record from between 1100 and 800 B.C. shows a decline in art; pottery from this period is typically more crude, burial sites are far less elaborate, and there are none of the massive palaces and temples that characterized the architecture of Crete and Mycenae. Most significantly, the Greeks appear to have become illiterate again;

11. The Archaic Period : 700-480 B.C. Individual city-states and their colonies prosper, giving rise to centers of political, religious, philosophic and artistic development. Many of the Greek cities in the mainland, Aegean islands, and the Ionian coast are ruled by "tyrants", strong-willed men who rule, not by constitutional authority, but by popular support. Aethens was the richest and most powerful of these city state. Around 6th century BC Solon, a "moderate" dictator of Athens, wrote the first table of laws. For the first time in history, imprisonment was considered a punishment while before only death or dismemberment were considered.

12. Greece does not have much available farmland and it is very dry. The ancient Greeks founded colonies all over the Mediterranean sea. (map of Greek settlements, 7 th century BC)

13. Roma was founded in 753 BC and began to expand its territory Roma was founded in 753 BC and began to expand its territory….

14. Numbers Until 600 BC numbers were written differently in different city state. The Greeks, like the Egyptians, associated a symbol to each number.

15. We have very few documents from early Greek civilization. They did not preserve their documents in burial sites, like the Egyptians and the Babylonians did, and so we only rely on what historians from later periods wrote about Greek civilization and on the translations and copies of these documents.

16. After 600 BC all the city states used the same system of numbers. They used letters to denote numbers, both upper case or lower case. Since the Greek alphabet has only 24 symbols, they introduced three new symbols. The symbols for 6, 90 and 900 are not in the the Greek alphabet.

17. In early Greek mathematics, unit fractions were generally the only ones present. This meant that the only numerator they could use was the number 1. The notation was a mark above or to the right of a number to indicate that it was the denominator of the number 1. For unit fractions, a diacritical mark (a prime) was placed after the denominator of the fraction. So,

18. We have basically no record of Greek arithmetic. But Arithmetic or computational skill was not one of the Greeks’ contribution to the History of Mathematics…