Hippasus Hippasus of Metapontum Hippasus of Metapontum (/ˈhɪpəsəs/; Greek: Ἵππασος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. Life[edit] Little is known about the life of Hippasus. Doctrines[edit] A scholium on Plato's Phaedo notes him as an early experimenter in music theory, claiming that he made use of bronze disks to discover the fundamental musical ratios, 4:3, 3:2, and 2:1.[13] Irrational numbers[edit] Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning.[14] Iamblichus gives a series of inconsistent reports. See also[edit] Incommensurable magnitudes References[edit] External links[edit]
Orphism (religion) Set of ancient Greek and Hellenistic religious beliefs Orphic mosaics were found in many late-Roman villas In order to maintain their purity following initiation and ritual, Orphics attempted to live an ascetic life free of spiritual contamination, most notably by adhering to a strict vegetarian diet that also excluded broad beans. The belief that Pythagoreanism was a subset or direct descendant of Orphic religion existed by late antiquity, when Neoplatonist philosophers took the Orphic origin of Pythagorean teachings at face value. Proclus wrote: The Orphic theogonies include: The "Protogonos Theogony", lost, composed c. 500 BC, which is known through the commentary in the Derveni papyrus and references in classical authors (Empedocles and Pindar).The "Eudemian Theogony", lost, composed in the 5th century BC. The Orphic Hymns are 87 hexametric poems of a shorter length composed in the late Hellenistic or early Roman Imperial age. Orphic Egg Fulińska, Agnieszka (2014).
Pythagoras Greek philosopher (c. 570 – c. 495 BC) Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC)[b] 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. The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis, which holds that every soul is immortal and, upon death, enters into a new body. Life Early life There is not a single detail in the life of Pythagoras that stands uncontradicted. Reputed travels Alleged Greek teachers In Croton Family and friends Death Teachings
Simonides of Ceos His general renown owes much to traditional accounts of his colourful life, as one of the wisest of men; as a greedy miser; as an inventor of a system of mnemonics; and also the inventor of some letters of the Greek alphabet (ω, η, ξ, ψ).[2] Such accounts include fanciful elements, yet he had a real influence on the sophistic enlightenment of the classical era.[3] His fame as a poet rests largely on his ability to present basic human situations with affecting simplicity.[4] In the words of the Roman rhetorician Quintilian (55–100 AD): Simonides has a simple style, but he can be commended for the aptness of his language and for a certain charm; his chief merit, however, lies in the power to excite pity, so much so that some prefer him in this respect to all other writers of the genre.[5] He is popularly associated with epitaphs commemorating fallen warriors, as for example the Lacedaemonians at The Battle of Thermopylae: Biography[edit] Early years: Ceos and Athens[edit] The inventor[edit]
Irrational number The famous mathematical constant pi (π) is among the best known irrational numbers and is much represented in popular culture In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational.[1] History[edit] The number is irrational. Ancient Greece[edit] Start with an isosceles right triangle with side lengths of integers a, b, and c. Greek mathematicians termed this ratio of incommensurable magnitudes alogos, or inexpressible. The discovery of incommensurable ratios was indicative of another problem facing the Greeks: the relation of the discrete to the continuous. India[edit] Middle Ages[edit]
Pythagoras A 6th-century BCE Greek philosopher and mathematician, originally from Samos (an island off the coast of Asia Minor settled by the Greeks), and born about 570 BCE, he left home and "by his own choice / Became an exile" (Ovid 354) around 530 BCE to escape the tyranny of the autocrat Polycrates. He lived in southern Italy, influencing city politics until the turn of the century when the citizens revolted against his influence and forced him to settle in Metapontum instead. Followers venerated him and they formed some sort of quasi-religious order. Although he did not set down his ideas in written form, Pythagorean centers sprang up throughout the Greek mainland during the 5th century BCE, including in Thebes and Athens, so he certainly influenced Socrates and therefore Plato. Legends include an instance of a superhuman voice wishing Pythagoras good morning as he was crossing the river Casas, and his being able to appear in both Croton and Metapontum on the same day at the same hour.
Magna Graecia Cities of Magna Graecia and other Greek settlements in Italy (in red) Antiquity[edit] According to Strabo, Magna Graecia's colonization had already begun by the time of the Trojan War and lasted for several centuries.[2] In the 8th and 7th centuries BC, for various reasons, including demographic crises (famine, overcrowding, etc.), the search for new commercial outlets and ports, and expulsion from their homeland, Greeks began to settle in southern Italy (Cerchiai, pp. 14–18). Also during that period, Greek colonies were established in places as widely separated as the eastern coast of the Black Sea, Eastern Libya and Massalia (Marseille). They included settlements in Sicily and the southern part of the Italian Peninsula. With colonization, Greek culture was exported to Italy, in its dialects of the Ancient Greek language, its religious rites and its traditions of the independent polis. Following the Pyrrhic War in the 3rd century BC, Magna Graecia was absorbed into the Roman Republic.
Eleusinian Mysteries Votive plaque depicting elements of the Eleusinian Mysteries, discovered in the sanctuary at Eleusis (mid-4th century BC) The rites, ceremonies, and beliefs were kept secret and consistently preserved from a hoary antiquity. The initiated believed that they would have a reward in the afterlife.[5] There are many paintings and pieces of pottery that depict various aspects of the Mysteries. Since the Mysteries involved visions and conjuring of an afterlife, some scholars believe that the power and longevity of the Eleusinian Mysteries came from psychedelic agents.[6] Mythology of Demeter and Persephone[edit] The Mysteries are related to a myth concerning Demeter, the goddess of agriculture and fertility as recounted in one of the Homeric Hymns (c. 650 BC). According to the myth, during her search Demeter traveled long distances and had many minor adventures along the way. Mysteries[edit] Participants[edit] To participate in these mysteries one had to swear a vow of secrecy. Secrets[edit]
Square root of 2 "Pythagoras's constant" redirects here; not to be confused with Pythagoras number The square root of 2, often known as root 2, radical 2, or Pythagoras' constant, and written as Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. 1.41421356237309504880168872420969807856967187537694807317667973799... The square root of 2 (number line not to scale). The quick approximation 99/70 (≈ 1.41429) for the square root of two is frequently used. History[edit] Babylonian clay tablet YBC 7289 with annotations. The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of in four sexagesimal figures, 1 24 51 10, which is accurate to about six decimal digits:[1] . Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. The value of .
Pythagoras and His Theory of Reincarnation SCIENCE - SPIRITUALITY, 17 Jun 2013 Igor Bukker - Pravda The name of Pythagoras is known to all from school, but many people associate this name with a theorem in geometry. Meanwhile, this ancient Greek philosopher, mathematician and mystic was the first man, who coined such terms as “philosopher” and “philosophy” (in our modern sense). Pythagoras was born in Samos, a town located on the island of the same name in the Aegean Sea, which was one of the most prominent and well-known centers of the Hellenic world in the VI century BC.. Iamblichus, in contrast to other ancient authors, gave a different spelling of the name of Pythagoras’ father – Mnemarh. Mnesarchus gave that name to his wife after visiting the oracle of Apollo in Delphi to inquire about a voyage to Syria. Igor Surikov explains why such interpretation is unlikely, “Pythagoras is a common ancient Greek name, which appears for the most part without any connection with Apollo and Delphi. Go to Original – pravda.ru
Italiotes Groups within the Italian peninsula The Italiotes (Greek: Ἰταλιῶται, Italiōtai) were the pre-Roman Greek-speaking inhabitants of the Italian Peninsula, between Naples and Sicily. Greek colonization of the coastal areas of southern Italy and Sicily started in the 8th century BC and, by the time of Roman ascendance, the area was so extensively hellenized that Romans called it Magna Graecia, "Greater Greece". The Latin alphabet is a derivative of the Western Greek alphabet used by these settlers, and was picked up and adopted and modified first by the Etruscans and then by the Romans. Italiote League[edit] Tarentum controlled the Italiote League from about the end of the 5th century BC and levied troops from the Greek cities.[1] Dionysius I of Syracuse conquered southern Italy (Magna Graecia), crushing the Italiote (Greek) League at the Battle of the Elleporus and destroying Rhegium.[2] See also[edit] Notes[edit] References[edit]