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An ionian.
1. What are the advantages of Ionia in Greece, which can become an early cultural center? 2. Why is Ionia the birthplace of Greek philosophy? 3. What was the final result of the Ionian city-state uprising? 4. What are the main schools of Greek mathematics in Athens? What are their main mathematical ideas? 5. What is the Lower Ionian Model? What are the advantages of Ionia, the predecessor of Greece, as an early cultural center?

Ionia is located on the west coast of the Asian Peninsula and the east coast of the Aegean Sea. In classical times, there were Miletus and other 12 city-states, which were called "Twelve City-States of Ionia" in history. Historically, this place is far from the Greek peninsula and is the place where Greece colonized and expanded. But from the "dark ages", Ionia became the cultural center of Greece, with Thales (the first Greek philosopher, anaximander (the originator of cartography, Heraclitus and Pythagoras), Araxagora (the originator of atomism), Herodotus (the father of western historiography), Hippocrates (the father of western medicine) and Sappho (the famous Greek poetess, Therefore, the reasons for the prosperity of Ionian culture are worth exploring.

First of all, Ionia inherited Mycenae's civilization.

About 1 100 years ago, the Greek peninsula was invaded by Dorians in the north, Mycenae civilization was destroyed, and society returned to the era of clan society. People call this era of Dorian invasion the "dark age". The Greek civilization of this era was undoubtedly dealt a heavy blow. However, due to a large number of immigrants, the culture and customs of Mycenae were preserved.

Before the Dorian invasion, the Greek peninsula was inhabited by Ionians and Ionians, as well as earlier Pilaski and others. When Dorians went south, a large number of Ionians and Ionians chose to move out of the Greek Peninsula and reach some islands around the Aegean Sea and Asia Minor. Among them, those who arrived in Xiaoya were collectively called Ionia. For the Greeks, the climate of Ionia is very pleasant. Herodotus called it "the region with the most beautiful climate and season, whether it is the north, the south, the east or the west, it is not as blessed as Ionia." In the end, Greek immigrants established twelve large city-states here, and some smaller city-states or settlements.

Ionians brought Greek cultural customs to the Asian peninsula. For example, among the six tribes in Miletus, four are the tribal names of Attica, and the other two are from Thessaly and Biotia in northern Greece; The patron saint of Miletus is still Athena; Miletus preserved a lot of traditions, customs and religions in Attica. Therefore, in the dark ages, Ionians migrated to Asia, which preserved Mycenae culture to some extent and prepared for the rise of Ionia.

Around the 9th century BC, Ionian culture began to flourish, and the famous Homer epic appeared in this era. After the Trojan War, some stories and legends about the incident spread in Asia. In the dark ages, it is said that these stories and legends were arranged by Homer and formed the early Homer epic.

In addition to Homer's epic, hesiod, another literary master, appeared in Ionia. He wrote two important works, Work and Time and Shenpu. He is the "father of Greek Oracle poetry" in Greece. His works arranged Mycenae's religious culture and formed a certain system of Greek myths and legends. In ancient times, Aesop, Sappho and other celebrities appeared here. Aesop is a famous fable writer. It is said that he wrote the earliest Aesop's Fables. Sappho was the earliest poetess in Greece.

Second, the importance of geographical location and the prosperity of industry and commerce.

Ionia's geographical position is very special. Located at the westernmost tip of Asia, it is the only place for ancient Asian-European traffic and guards the sea passage from the Mediterranean to the Black Sea. The superior traffic location enables Ionian industry and commerce to develop rapidly. As early as the Mycenaean civilization, Troy in Asia was prosperous and civilized because of the prosperity of industry and commerce. At that time, Troy became a city rich in gold and bronze by taxing ships passing through the Turkish Strait.

After the establishment of the Ionian polis, they enjoyed the advantages of Troy in the past. Miletus, Ephesus and Bokeya are located at the estuaries of Maiande River, Kester River and Helmas River respectively, which control the traffic from Aegean Sea to the interior of Asia. Miletus and Ephesus are also the distribution centers of goods in Italy and Greece. Theos and Samos control the coastal routes from north to south. Among the twelve city-states of Ionia, Miletus has the most developed commerce. There are four seaports, each of which can berth a fleet. It can be said that the advantages of maritime traffic are very obvious.

During the colonial period in ancient times, the Ionian city-states actively established colonies in the Turkish Strait and the Dark Coast to further control the traffic fortress between Asia and Europe. Among them, Miletus is the most active. In the 5th century, the Greeks established 90 colonies in the Black Sea, most of which belonged to Miletus. These cities are famous for Istrus at the mouth of the Danube River, Boris Tinis at the mouth of the Dnieper River, Olbia at the mouth of the Bouguer River and Tiilas at the mouth of the Dniester River. The earliest colony in the Turkish Strait was also founded by Miletus.

With this advantage, most Ionians are engaged in navigation, commerce, shipbuilding and fishing. Residents on land can also engage in grain, olives, grapes and so on. And animal husbandry is developed in mountainous areas. From the 8th century to the 7th century, Miletus became the production center of textile, printing and dyeing, metallurgy and shipbuilding. It produces wool, linen fabrics, pottery, wine, olive oil and other civilizations as well as the Greek world. In the 7th century, Miletus, Pokia and Ephesus began to introduce minted currency to adapt to the development of commodity economy.

The prosperity of industry and commerce is the basis of the prosperity of Ionian culture. Thales, the first Greek philosopher, founded the famous Miletus School. He was born in a merchant family. He can predict the price of Athens olives according to the astronomical phenomena to prove that he is good at business. Pythagoras was also born in a merchant family, while Herodotus and Heraclitus were born in a noble family. Superior family conditions enable them to devote more energy to cultural creation and scientific exploration, and at the same time provide economic guarantee for their long-distance travel around the Mediterranean.

Third, absorb the achievements of other civilizations.

Because of Ionia's special geographical location and industrial and commercial prosperity, people here have more opportunities to get in touch with the brilliant achievements of ancient Egypt, the two river basins and other civilizations. Greek civilization itself is a derivative civilization, and it is a marine civilization that has absorbed the foundation of the two major civilizations. Greek science, religion, art and writing were all influenced by ancient countries such as Egypt, Phoenicia, Babylon, Assyria and Hittite.

Thales, the first Greek philosopher, traveled to West Asia and North Africa in his early years. He learned the knowledge of observing solar eclipses and calculating the distance between ships at sea in Babylon, learned the Phoenician thought of exploring material elements, and realized the distribution and rules of measuring land in ancient Egypt. Many of his mathematical knowledge comes from ancient Egypt and the two river basins. Later, he put forward six theorems of plane geometry, which was his sublimation of these mathematical knowledge.

Pythagoras after Thales studied hieroglyphics and Egyptian mythology, history and religion in ancient Egypt. Heraclitus of the Festus School once taught in Persian palaces; Hippocrates, the father of medicine, once benefited Asia, the Caspian Sea and North Africa and absorbed medical knowledge from many countries, so he was called a master. Herodotus and others all had the experience of traveling in the East, which undoubtedly broadened his horizons and enriched his knowledge.

Herodotus is known as "the father of western historiography". The History of Persian War written by Herodotus covers the whole Mediterranean and Black Sea world, showing the history, customs and geography of more than 20 countries and nationalities. The geography of ancient Greece is very developed. The geography of ancient Greece originated from Ionia, which is related to the extensive travel of Ionians.

The cultural prosperity of Ionia is inseparable from its special geographical location. However, after the Persian War, Asian city-states were basically ravaged and occupied by the Persian Empire, and many literati returned to Athens, the former residence of Ionia, with rich cultural knowledge. Since then, Athens has replaced Ionia as the center of Greek culture. However, after the demise of the Persian Empire, the advantages of Asia Minor reappeared. In the Hellenistic era, Aristak, Sipakush, Epicurus and other famous scientific and philosophical figures all appeared here.

Why Ionia is the birthplace of Greek philosophy?

Ionia, located in the Asian Peninsula (southwest coast of Turkey), is named after Ionian people settled here. In the history of ancient Greece, Ionia was an extremely important place and the center of early Greek city-state civilization. The science, philosophy and history of ancient Greece were born here, producing famous cultural figures such as Thales, Heraclitus, Pythagoras, Yudhoyono and Herodotus. What made Ionia the center of early Greek culture? Taking Thales as an example, we made some systematic analysis.

First of all, Ionia's economic prosperity

The geographical location of Ionia is very important. Located in the bridgehead of Asia and Europe, the coastline is tortuous and there are many good ports. Miletus is the most prosperous of the twelve city-states in Ionia. Located at the mouth of Mendes River, it is the center of handicraft, navigation and commerce on the east coast of Aegean Sea. The superior geographical position makes Ionia's industry and commerce prosper, and the prosperity of industry and commerce lays the foundation for the prosperity of culture.

Schematic diagram of Ionian location

Miletus is one of the Greek city-states that embarked on democratic politics earlier. Merchant rule replaced clan aristocratic politics earlier, which provided good conditions for the development of commerce. According to the inscription on the Miletus Punishment Act, Miletus implemented a civil service system similar to Athens in 380 BC, with the shell exile law. The relaxation of politics and the development of business provide the necessary social soil for the freedom of thought and the rise of academic activities.

Miletus amphitheater

Take Thales as an example. Although he is a nobleman, his family is engaged in business, and Thales himself is a businessman. Thales can prove his ability to make money by predicting the price of Athens olives according to the astronomical phenomena. Except Thales, Pythagoras came from a wealthy family, and Herodotus and Heraclitus were nobles. A solid economic foundation gives them time and energy to explore scientific, philosophical and historical knowledge, and provides funds for their long-distance travel.

Thales

Second, Ionia can better absorb the culture of Egypt and the two rivers.

Ionia is located in Asia, which is the closest to the two rivers civilization and Egyptian civilization. Ancient Greek civilization is a derivative civilization influenced by these two civilizations, and its writing, science, mythology and literature are all influenced by these two civilizations. The main channels of communication between Greek civilization and the two rivers civilization are Asia Minor, Syria-Palestine region and Cyprus, so these regions have developed their own unique cultures and become a veritable "golden coast".

The ancient city of Eiffel in Ionia.

Thales traveled to West Asia and North Africa in his early years. In Babylon, he learned the knowledge of observing solar eclipses and measuring the distance of ships at sea, learned the Phoenician thought of exploring material elements, and learned the distribution and law of measuring land in ancient Egypt. Thales learned a lot of mathematics from the two river basins and ancient Egypt. He put forward six theorems of plane geometry, such as "the diameter bisects the circumference", "the equal sides of a triangle are equal angles" and "the intersection of two straight lines and the equal vertex angle". According to historical records, he once measured the height of ancient Egyptian pyramids according to similar triangles's theorem. He put forward that "water is the source of all things", and his views came from the religious myths of ancient Egypt. The priests in ancient Egypt once declared that "the earth rises from the bottom of the sea", while Thales said that the earth floats on water.

Method of measuring pyramids

Besides Thales, Pythagoras, Heraclitus, Herodotus, etc. Everyone has the experience of traveling in the East. Pythagoras visited Thales and studied hieroglyphics and Egyptian mythology, history and religion in ancient Egypt. Heraclitus went to the Persian court to teach Greek culture; Herodotus traveled around the Mediterranean, and his History of Persian War is regarded as the world history of the Mediterranean.

Herodotus-Father of Western History

Generally speaking, both economically and culturally, the civilizations of ancient Egypt and the two river basins have had a far-reaching impact on Ionia. Of course, this is all because of Ionia's special geographical location. After the rise of the Persian Empire, the Persian Empire launched a long-term war against Greece, which eventually led to the decline of Ionia. Since then, the cultural center of Greece has moved to Athens.

What was the final result of the Ionian city-state uprising?

In 500 BC, Alistair, the tyrant of Miletus, the largest city-state of Ionia in Asia Minor, provoked Persia to attack Naxos in the Aegean Sea, but failed. Fearing the punishment of Persians, he took advantage of the people's resistance to Persian rule to launch an uprising in all the city-states of Ionia. Miletus attacked first, and other States responded one after another, and the tyrants of the States supported by Persia were overthrown one after another. The Ionian city-state uprising led by Miletus opened the prelude to the war between the Greek city-state and the Persian Empire.

After the Ionian city-state uprising, Alistair went to Sparta and Athens for help. Sparta, which had no overseas economic interests and no naval power, weighed the pros and cons and rejected the aid on the grounds of Taiyuan. Athens is different. Based on their own interests, the Athenians refused the Persian Governor Sardis's request for Athens to give "water and soil" (that is, the request for surrender) and his "order" to welcome the exiled tyrant Hippocrates back to Athens. Knowing that war with Persia was inevitable, they decided to send 20 warships to help their compatriots liberate. Eli, once an ally of Miletus, sent five warships.

In the summer of 499 BC, reinforcements from Athens and Eliot arrived in Asia Minor. Together with the uprising team of the Ionian city-state, they set out from Ephesus and captured Sardis, the residence of the Persian governor, and then retreated after burning the city, but were defeated by the Persian army following them at Ephesus. Athens and Ellet withdrew their reinforcements, and the Ionian city-states continued their struggle. Soon, the Greeks, the Kalian Greek city-states and the Cypriots rose up against the Persian rule.

After suppressing the uprising of Cyprus and Greeks, Persia concentrated Lu Haijun to attack Miletus in 497 BC. The joint fleet of Ionian countries was destroyed by Phoenician fleet near Rade Island because of disagreement and uncoordinated actions. Miletus was immediately besieged, and the residents bravely defended for more than a year, and finally fell in 495 BC. The city was burned, most of the citizens died, and the remaining thousands of women and children were taken captive to Susa, the capital of Persia. The fall of Miletus left an unforgettable impression on the Athenians, who mourned the disaster suffered by their compatriots in various ways. When Frunijos's tragedy "The Fall of Miletus" was staged in Athens Theatre, the audience wailed. Frunijos was fined 1 1,000 Derlager Mai, and no one was allowed to perform the play again.

In the second year after the fall of Miletus, other insurgent city-states were successively suppressed by Persia. The Greek city-state uprising in Asia Minor, which lasted for six years, was a complete failure.

Darius decided to conquer Balkan Greece by force after suppressing the uprising of Greek city-states in Asia Minor. Athens and Ellet's aid to Miletus became an excuse for Persian attack.

What are the main schools of Greek mathematics in Athens? What are their main mathematical ideas?

Ionian school

Ionian school, also known as Miletus school, refers to the school formed in Ionian in ancient Greece, which was founded in the 7th century BC and represented by Thales.

The Ionian school denies that God is the creator of the world, thinks that water is the foundation of all things, advocates the laws of nature, and scientifically demonstrates some basic theorems of mathematics. When Thales visited Egypt, he used similar triangles's principle to measure the height of the pyramids and accurately predicted the solar eclipse on May 28th, 585 BC. He began to prove the proposition in the history of mathematics development, and the main achievements are as follows: the diameter of a circle is equal to the circumference; The two base angles of an isosceles triangle are equal; Two straight lines intersect and the vertex angles are equal; The sides of similar triangles are proportional; Right angles are equal to each other; The circumference angle of a semicircle is a right angle, etc. According to legend, Thales theorem is that if two angles of two triangles correspond to one side, then the two triangles are congruent.

The Ionian school also came to the basic arithmetic definition that any natural number is the sum of several "1", and actively applied their theory to practical measurement, laying the foundation for the development of mathematics. The main members of the Ionian School are anaximander, Anaximenes, Anassa Golas, etc.

Pythagoras school

Pythagoras School refers to a school founded by Pythagoras, an ancient Greek philosopher, mathematician, astronomer and music theorist around 520 BC. This school is a combination of religion, politics and scholarship. Tight organization, consistent philosophical beliefs and political theories, strict training and high academic level. Pythagoras learned from anaximander of the Ionian School the knowledge of astronomy and mathematics handed down from Egypt and Babylon. The school attaches great importance to mathematics and tries to explain everything with numbers. It not only thinks that everything contains numbers, but also says that everything is numbers, claiming that God rules the universe with numbers, which is obviously different from other schools.

The greatest contribution of Pythagoras school is to discover incommensurable measures and irrational numbers, break through the traditional concept that all numbers are only natural numbers and fractions, and promote the development of mathematics. In geometry, five kinds of regular polyhedrons are found, which correspond to some basic elements of nature and are studied as mathematical problems. In addition, Pythagoras and his disciples have made great progress in logical proof, and their work constitutes the predecessor of Euclid's axiomatic system.

Hippasus, Philolaus, arshi Tass and others are famous scholars of the Pythagorean school. They made the most advanced achievements at that time, but they kept the new achievements secret, so they failed to get the timely influence of the masses. Later, due to political turmoil, the disciples were lost and gradually disappeared in the middle of the 4th century BC.

Homo sapiens school

Homo sapiens school, also known as sophistry school, existed in ancient Greece from the 5th century BC to the 4th century BC and was active in Athens. Members of the school often go to mass gatherings to give speeches, and their occupation is to teach rhetoric, eloquence, grammar, logic, mathematics, astronomy and other knowledge. The center of its mathematical research is drawing with two tools, ruler and compass, which are not calibrated. The so-called geometric drawing has three major problems:

Divide any angle equally;

Double cubes are found one by one as a cube, so that its volume is twice that of a known cube;

Turn a circle into a square and find a square so that its area is equal to that of a known circle.

Although these three problems proved to be impossible tasks, many new branches of mathematics were developed, such as conic curves, cubic and quartic algebraic curves and secant. The secant was created by Pias, a member of this school, to divide any angle equally. When Ann Di Feng studied the problem of turning a circle into a square, she put forward an "exhaustive method", that is, by doubling the number of sides of a regular polygon inscribed in a circle, the polygon and the circle were merged into one, which became the pioneer of Archimedes' cyclotomy and the prototype of modern limit theory.

Elijah school

Elijah School was formed in Elijah area of ancient Greece, represented by parmenides, Zhi Nuo and others. They believe that the origin of the world is "existence", and all existence must be "one" and static, and there is nothing that is opposite or contradictory to existence. Zhi Nuo tried to expose the contradictions in sports for the first time, and put forward four famous paradoxes: dichotomy, Achilles chasing turtles, flying arrows at rest, and playground problems.

These paradoxes have caused the discussion of many basic problems in philosophy, physics and mathematics, and played an important role in promoting the development of concepts such as discreteness and continuity, finiteness and infinity, time and space.

Atomism school

The atomism school was formed in Gu Xi from the 5th century BC to the 4th century BC, with democritus and his teacher Le Gups as its representatives.

The atomism school thinks that matter is unified and homogeneous; It contains many inseparable small particles, which are always in motion and form various compounds through collision and recombination. Democritus applied the atomic viewpoint to mathematics, and thought that line segments, areas and solids were all composed of finite atoms that could not be subdivided, so the problem of volume calculation was transformed into the problem of atomic collection. On this basis, he calculated the volumes of cones and pyramids. The first conclusion is that the volume of cones is one-third of the volume of cylinders with equal bottoms and equal heights. The method of atomism has been appreciated by contemporary and later scholars. A Di Feng developed this idea when calculating the area of a circle. Archimedes made it precise with rigorous theory. The method used by Kepler in the16th century to find the circular area still has the heritage of atomism.

Athens school

Athens school refers to the school established in Athens, ancient Greece, which prevailed from the 5th century BC to the 4th century BC. The main personnel and their thoughts are concentrated in Plato Academy and Aristotle Academy, so they are often called Plato School and Aristotle School respectively.

Plato was a great philosopher in Athens. He studied under Socrates and was greatly influenced by the teacher's logical thought. He founded a college in Athens around 387 BC, and strongly advocated geometric research and logical proof in teaching. It is said that "those who don't know geometry are not allowed in" at the entrance of the academy. He insisted on precise definition, clear assumptions and strict reasoning, which promoted the scientification of mathematics and trained many mathematicians. Among them, Meiniche Muse, who was the first to systematically study conic curves, used de Nostradamus Toth, Titus, eudoxus, Aristotle and so on. Eudoxus was a student of Plato. He was the first Greek scientist to introduce spherical astronomy and describe constellations. He founded the proportional theory and exhaustive method in mathematics, deeply studied the problem of "middle-end ratio", and first came up with "Archimedes axiom", proved some propositions in modern limit theory, and also distinguished analytical method from comprehensive method. His theory is very helpful to the completion of Euclid's Elements of Geometry. He established his own pure geometry school in Jikus, which is usually called Eudoxus School.

Aristotle and Plato lived together for 20 years, and then separated because of different philosophical views. Around 335 BC, he established his own school and taught in Lu Garden in Athens, so this school is usually called Lu Garden School. Aristotle, the founder of formal logic, discussed the basic principles of mathematics and gave the definitions of point, line and surface. Aldous Moss of this school wrote the history of arithmetic, geometry and astronomy, and was an early historian of science.

Alexander school

Alexandria school refers to the school established by ancient Greece in Alexandria, Egypt. The early period was 146 BC, represented by Euclid, Archimedes, Apollonius, Eratosthenes and others. Late BC 146-AD ⑥4 1 year, represented by Helen, Menelaus, Ptolemy, Diophantine, Pappus and Xu Pathias.

The characteristics of Alexandria school are: geometry is independent from philosophy, developing from empirical science of experiment and observation to deductive science, and making mathematics highly abstract, pushing Greek mathematics to its peak. This school has outstanding achievements in geometry, trigonometry and algebra.

After the 7th century BC, geometry accumulated a wealth of data, and Euclid's Elements of Geometry was comprehensively sorted out, which became the first model to establish a deductive mathematical system by axiomatic method. Euclid gave lectures in Alexandria around 300 BC, which laid a solid foundation for the development of Alexandria school and the whole Greek mathematics.

Archimedes studied in Alexandria in his early years and kept close contact with scholars there all his life. His contributions to surface area and volume calculation, spiral research, center of gravity measurement and large number notation have become important achievements of various branches.

Apollonius studied in Alexandria and then taught there. His theory of conic curve completely covers the properties of conic curve and plays an important role in the development and prosperity of Greek mathematics.

In trigonometry, Ptolemy's Selected Astronomies and Menarus's Theory of Sphere became the representative works of Alexander School, and summarized and discussed plane trigonometry and spherology respectively.

In the process of establishing algebra, Diophantine's arithmetic is unique, which makes algebra completely out of geometric form and tries to study symbolic algebra.

Other scholars in Alexander's later period made a lot of comments and repairs on the previous work, and also made contributions to the measurement and geometry of spheres. After 390 AD, the library of Alexandria was burned down, and Pathias was killed in 4 15 AD, which marked the decline of mathematics in Alexandria. ⑥ In 4 1 year, Alexandria was captured by Arabs, and the Alexandria School ended.

What is the predecessor of the lower Ionian model?

Lower Ionian mode is the predecessor of natural major. According to relevant data, natural major is usually referred to as C major for short, that is, the Ionian mode in the Middle Ages is one of the modes.