Greek mathematics in the context of "Eratosthenes"

Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to the east. The Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, and the Sea of Crete and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean basin, spanning thousands of islands and nine traditional geographic regions. It has a population of over 10 million. Athens is the nation's capital and largest city, followed by Thessaloniki, Patras and Heraclion.

Greece is considered the cradle of Western civilisation and the birthplace of democracy, Western philosophy, Western literature, historiography, political science, major scientific and mathematical principles, theatre, and the Olympic Games. The Ancient Greeks were organised into independent city-states, or poleis (singular polis), that spanned the Mediterranean and Black seas. Philip II of Macedon united most of present-day Greece in the fourth century BC, with his son Alexander the Great conquering much of the known ancient world from the Near East to northwestern India. The subsequent Hellenistic period saw the height of Greek culture and influence in antiquity. Greece was annexed by Rome in the second century BC and became an integral part of the Roman Empire and its continuation, the Byzantine Empire, where Greek culture and language were dominant. The Greek Orthodox Church, which emerged in the first century AD, helped shape modern Greek identity and transmitted Greek traditions to the wider Orthodox world.

Pappus of Alexandria (/ˈpæpəs/ ; Ancient Greek: Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c.  350 AD) was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a mathematics teacher to higher level students, one of whom was named Hermodorus.

The Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics.

Diophantus of Alexandria (Ancient Greek: Διόφαντος, romanized: Diophantos) (/daɪoʊˈfæntəs/; fl. 250 CE) was a Greek mathematician who was the author of the Arithmetica in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic equations.

Although Joseph-Louis Lagrange called Diophantus "the inventor of algebra" he did not invent it; however, his exposition became the standard within the Neoplatonic schools of Late antiquity, and its translation into Arabic in the 9th century AD and had influence in the development of later algebra: Diophantus' method of solution matches medieval Arabic algebra in its concepts and overall procedure. The 1621 edition of Arithmetica by Bachet gained fame after Pierre de Fermat wrote his famous "Last Theorem" in the margins of his copy.

Posidonius (/ˌpɒsɪˈdoʊniəs/; Ancient Greek: Ποσειδώνιος Poseidṓnios, "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (c. 135 – c. 51 BC), was a Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher native to Apamea, Syria. He was considered the most learned man of his time and, possibly, of the entire Stoic school. After a period learning Stoic philosophy from Panaetius in Athens, he spent many years in travel and scientific researches in Spain, Africa, Italy, Gaul, Liguria, Sicily and on the eastern shores of the Adriatic. He settled as a teacher at Rhodes where his fame attracted numerous scholars. Next to Panaetius he did most, by writings and personal lectures, to spread Stoicism to the Roman world, and he became well known to many leading men, including Pompey and Cicero.

His works are now lost, but they proved a mine of information to later writers. The titles and subjects of more than twenty of them are known. In common with other Stoics of the middle period, he displayed syncretic tendencies, following not just the earlier Stoics, but making use of the works of Plato and Aristotle. A polymath as well as a philosopher, he took genuine interest in natural science, geography, natural history, mathematics and astronomy. He sought to determine the distance and magnitude of the Sun, to calculate the diameter of the Earth and the influence of the Moon on the tides.

Pythagoras of Samos (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.

In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wisdom"). Historians debate whether Pythagoras made these discoveries and pronouncements, as some of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors, such as Hippasus and Philolaus.

Perga or Perge (Hittite: Parha, Greek: Πέργη Perge, Turkish: Perge) was originally an ancient Lycian settlement that later became a Greek city in Pamphylia. It was the capital of the Roman province of Pamphylia Secunda, now located in Antalya Province on the southwestern Mediterranean coast of Turkey. Today its ruins lie 15 kilometres (9.3 mi) east of Antalya.

It was the birthplace of Apollonius of Perga, one of the most notable ancient Greek mathematicians for his work on conic sections. A unique and prominent feature for a Roman city was the long central water channel in the centre of the main street which contained a series of cascading pools and which would have been remarkable even today in a semi-arid area where summer temperatures reach over 30 degrees Celsius.

A sophist (Greek: σοφιστής, romanized: sophistēs) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics and mathematics. They taught arete, "virtue" or "excellence", predominantly to young statesmen and nobility.

The arts of the sophists were known as sophistry and gained a negative reputation as tools of arbitrary reasoning. Protagoras, regarded as the first of the sophists, became notorious for his claim to "make the weaker argument the stronger".