Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... (2nd millennium BC - 1st millennium BC - 1st millennium) The 6th century BC started on January 1, 600 BC and ended on December 31, 501 BC. // Overview Monument 1, an Olmec colossal head at La Venta The 5th and 6th centuries BC were a time of empires, but more importantly, a... Europe in 450 The 5th century is the period from 401 - 500 in accordance with the Julian calendar in the Christian Era. ... The Mediterranean Sea is an intercontinental sea positioned between Europe to the north, Africa to the south and Asia to the east, covering an approximate area of 2. ...

Periodization

Classical Greek mathematics refers to the mathematics studied before the Hellenistic period, when Greek mathematics was limited to Greece. Greek mathematics studied from the time of the Hellenistic period onwards (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean. Greek mathematics from this point merged with Egyptian and Babylonian mathematics to give rise to the latter phase of Greek mathematics known as Hellenistic mathematics. Most of the mathematical texts written in Greek were found in Greece, Egypt, Mesopotamia, Asia Minor, Sicily and Southern Italy. The term Hellenistic (established by the German historian Johann Gustav Droysen) in the history of the ancient world is used to refer to the shift from a culture dominated by ethnic Greeks, however scattered geographically, to a culture dominated by Greek-speakers of whatever ethnicity, and from the political dominance... On his way from Ecbatana to Babylon, Alexander the Great fights and crushes the Cossaeans. ... Greek (, IPA — Hellenic) has a documented history of 3,500 years, the longest of any single language within the Indo-European family. ... The term Hellenistic (derived from HéllÄ“n, the Greeks traditional self-described ethnic name) was established by the German historian Johann Gustav Droysen to refer to the spreading of Greek culture over the non-Greek peoples that were conquered by Alexander the Great. ... The Mediterranean Sea is an intercontinental sea positioned between Europe to the north, Africa to the south and Asia to the east, covering an approximate area of 2. ... Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. In contrast to the sparcity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since... Mesopotamia refers to the region now occupied by modern Iraq, eastern Syria, southeastern Turkey, and Southwest Iran. ... Anatolia (Greek: ανατολη anatole, rising of the sun or East; compare Orient and Levant, by popular etymology Turkish Anadolu to ana mother and dolu filled), also called by the Latin name of Asia Minor, is a region of Southwest Asia which corresponds today to... Sicily (Sicilia in Italian and Sicilian, Σικελία in Greek) is an autonomous region of Italy and the largest island in the Mediterranean Sea, with an area of 25,700 km² and 5 million inhabitants. ... Southern Italy, often referred to in Italian as the Mezzogiorno (a term first used in 19th century in comparison with French Midi ) encompasses six of the countrys 20 regions: Basilicata Campania Calabria Puglia Sicilia Sardinia Sicilia although it is geographically and administratively included in Insular Italy, it has a...

Achievements

Greek mathematics constitutes a major period in the history of mathematics, fundamental in respect of geometry and the idea of formal proof. Greek mathematics also contributed importantly to ideas on number theory, mathematical analysis, applied mathematics, and, at times, approached close to integral calculus. The Compendious Book on Calculation by Completion and Balancing The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge -- the deductive study of quantity, structure, space and change. ... Table of Geometry, from the 1728 Cyclopaedia. ... ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ... To meet Wikipedias quality standards, this article may require cleanup. ... This article deals with the concept of an integral in calculus. ...

Well-known figures in Greek mathematics include Pythagoras, a shadowy figure from the isle of Samos associated partly with number mysticism and numerology, but more commonly with his theorem, and Euclid, who is known for his Elements, a canon of geometry for many centuries. Pythagoras of Samos (Greek: Πυθαγόρας; circa 582 BC – circa 507 BC) was an Ionian (Greek) mathematician and philosopher, founder of the mystic, religious and scientific society called Pythagoreans. ... Samos (Greek Σάμος) is a Greek island in the Eastern Aegean Sea, located between the island of Chios to the North and the archipelagic complex of the Dodecanese islands to the South and in particular the island of Patmos and off the coast of Turkey, on what was formely known as... This article or section does not cite its references or sources. ... In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ... Euclid (also referred to as Euclid of Alexandria) (Greek: ) (c. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems...

The most characteristic product of Greek mathematics may be the theory of conic sections, largely developed in the Hellenistic period. The methods used made no explicit use of algebra, nor trigonometry. Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ... Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ...

Origins

Greek mathematics has origins that are presumed to go back to the 7th century BC, but are not easily documented. It is generally believed that it built on the computational methods of earlier Babylonian and Egyptian mathematics, and it may well have had Phoenician influences. (2nd millennium BC - 1st millennium BC - 1st millennium) The 7th century BC started on January 1, 700 BC and ended on December 31, 601 BC. // Overview Events Ashurbanipal, king of Assyria who created the the first systematically collected library at Nineveh A 16th century depiction of the Hanging Gardens of... Babylonia, named for its capital city, Babylon, was an ancient state in the south part of Mesopotamia (in modern Iraq), combining the territories of Sumer and Akkad. ... This article or section is in need of attention from an expert on the subject. ... Phoenicia was an ancient civilization centered in the north of ancient Canaan, with its heartland along the coastal plains of what is now Lebanon. ...

Greek mathematics proper is thought to have begun from the late 500s BC, when Thales and Pythagoras brought knowledge of Egyptian and Babylonian mathematics to Greece. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. Pythagoras stated the Pythagorean theorem and constructed Pythagorean triples algebraically, according to Proclus' commentary on Euclid. Centuries: 7th century BC - 6th century BC - 5th century BC Decades: 550s BC - 540s BC - 530s BC - 520s BC - 510s BC - 500s BC - 490s BC - 480s BC - 470s BC - 460s BC - 450s BC Events and trends September 13, 509 BC - The temple of Jupiter on Romes Capitoline Hill is... Thales of Miletus Thales of Miletus also known as Thales the Milesian (Θαλῆς ὁ Μιλήσιος), (ca. ... Pythagoras of Samos (Greek: Πυθαγόρας; circa 582 BC – circa 507 BC) was an Ionian (Greek) mathematician and philosopher, founder of the mystic, religious and scientific society called Pythagoreans. ... Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. In contrast to the sparcity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since... Table of Geometry, from the 1728 Cyclopaedia. ... Pythagoras of Samos (Greek: Πυθαγόρας; circa 582 BC – circa 507 BC) was an Ionian (Greek) mathematician and philosopher, founder of the mystic, religious and scientific society called Pythagoreans. ... In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ... The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... Proclus Lycaeus (February 8, 412 – April 17, 485), surnamed The Successor or diadochos (Greek Πρόκλος ὁ Διάδοχος Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major Greek philosophers (see Damascius). ... Euclid (also referred to as Euclid of Alexandria) (Greek: ) (c. ...

The high period

Mathematical developments took place in Greek-speaking centres as far apart as Egypt and Sicily, and with a high estimation of the intellectual and cultural status of mathematics (for example in the school of Plato). The Sand Reckoner by Archimedes, a resident of Syracuse, bespeaks a man who made major discoveries, and whose originality and accomplishments are commonly reckoned to be on par with those of Isaac Newton and C. F. Gauss. Sicily (Sicilia in Italian and Sicilian, Σικελία in Greek) is an autonomous region of Italy and the largest island in the Mediterranean Sea, with an area of 25,700 km² and 5 million inhabitants. ... For other uses, see Plato (disambiguation). ... The Sand Reckoner is probably the most accessible work of Archimedes, in some sense, it is the first research-expository paper. ... Archimedes (Greek: ) (c. ... Syracuse (Italian, Siracusa, ancient Syracusa - see also List of traditional Greek place names) is a city on the eastern coast of Sicily and the capital of the province of Syracuse, Italy. ... Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 _ February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ...

Greek mathematics and astronomy reached a rather advanced stage during Hellenism, with scholars such as Hipparchus, Posidonius and Ptolemy, capable of the construction of simple analogue computers such as the Antikythera mechanism. The term Hellenistic (established by the German historian Johann Gustav Droysen) in the history of the ancient world is used to refer to the shift from a culture dominated by ethnic Greeks, however scattered geographically, to a culture dominated by Greek-speakers of whatever ethnicity, and from the political dominance... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... The bust of Posidonius as an older man depects his character as a Stoic philosopher. ... A medieval artists rendition of Claudius Ptolemaeus Claudius Ptolemaeus (Greek: ; c. ... The Antikythera mechanism (main fragment) The Antikythera mechanism (Greek: Ο μηχανισμός των Αντικυθήρων transliterated as O mēchanismós tōn Antikythērōn) is an ancient mechanical analog computer (as opposed to digital computer) designed to calculate astronomical positions. ...

Transmission and the manuscript tradition

Although the earliest Greek language texts on mathematics that have been found were written after the Hellenistic period, many of these are considered to be copies of works written during and before the Hellenistic period. Nevertheless, the dates of Greek mathematics are more certain than the dates of earlier mathematical writing, since a large number of chronologies exist that, overlapping, record events year by year up to the present day. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries. Greek (, IPA — Hellenic) has a documented history of 3,500 years, the longest of any single language within the Indo-European family. ...

During the Middle Ages, Europe derived much of its knowledge of Greek mathematics via Islamic mathematics. The texts of Greek mathematics were for the most part preserved and transmitted in the Islamic world. The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... Islamic mathematics is the profession of Muslim Mathematicians. ...