|
Hippasus
Hippasus of Metapontum (; , ''Híppasos''; c. 530 – c. 450 BC) was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras, which was the norm in Pythagorean society. The few ancient sources who describe this story, however, either do not mention Hippasus by name (e.g., Pappus) or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Life Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hippasus Metapontinus - Illustrium Philosophorum Et Sapientum Effigies Ab Eorum Numistatibus Extractae
Hippasus of Metapontum (; , ''Híppasos''; c. 530 – c. 450 BC) was a Greeks, Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the Greek gods, gods for divulging this and crediting it to himself instead of Pythagoras, which was the norm in Pythagorean society. The few ancient sources who describe this story, however, either do not mention Hippasus by name (e.g., Pappus) or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Life Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irrational Numbers
In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being '' incommensurable'', meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio of a circle's circumference to its diameter, Euler's number ''e'', the golden ratio ''φ'', and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek colony of Crotone, Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia. Already during Pythagoras' life it is likely that the distinction between the ''akousmatikoi'' ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the ''mathematikoi'' ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus () and his master Porphyry (philosopher), Porphyry ( ) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the Greco-Roman mysteries, mystery schools of antiquity, the adherents, ''akou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diogenes Laërtius
Diogenes Laërtius ( ; , ; ) was a biographer of the Greek philosophers. Little is definitively known about his life, but his surviving book ''Lives and Opinions of Eminent Philosophers'' is a principal source for the history of ancient Greek philosophy. His reputation is controversial among scholars because he often repeats information from his sources without critically evaluating it. In many cases, he focuses on insignificant details of his subjects' lives while ignoring important details of their philosophical teachings and he sometimes fails to distinguish between earlier and later teachings of specific philosophical schools. However, unlike many other ancient secondary sources, Diogenes Laërtius tends to report philosophical teachings without trying to reinterpret or expand on them, and so his accounts are often closer to the primary sources. Due to the loss of so many of the primary sources on which Diogenes relied, his work has become the foremost surviving source on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metapontum
Metapontum or Metapontium () was an ancient city of Magna Graecia, situated on the gulf of Taranto, Tarentum, between the river Bradanus and the Casuentus (modern Basento). It was distant about 20 km from Heraclea (Lucania), Heraclea and 40 from Tarentum. The ruins of Metapontum are located in the frazione of Metaponto, in the comune of Bernalda, in the Province of Matera, Basilicata region, southern Italy. History Foundation Though Metapontum was an ancient ancient Greece, Greek Achaean colony, various traditions assigned to it a much earlier origin. Strabo and Gaius Julius Solinus, Solinus ascribe its foundation to a body of Pylos, Pylians, a part of those who had followed Nestor (mythology), Nestor to Troy. Justin (historian), Justin, conversely, tells us it was founded by Epeius of Phocis, Epeius; in proof of which the inhabitants showed, in a temple of Minerva, the tools which the hero had used to build the Trojan Horse. Another tradition, reported by Ephorus, says ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli; it also goes by other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras
Pythagoras of Samos (; 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 wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Gods
In ancient Greece, deities were regarded as immortal, anthropomorphic, and powerful. They were conceived of as individual persons, rather than abstract concepts or notions, and were described as being similar to humans in appearance, albeit larger and more beautiful. The emotions and actions of deities were largely the same as those of humans; they frequently engaged in sexual activity, and were jealous and amoral. Deities were considered far more knowledgeable than humans, and it was believed that they conversed in a language of their own. Their immortality, the defining marker of their godhood, meant that they ceased aging after growing to a certain point. In place of blood, their veins flowed with ichor, a substance which was a product of their diet, and conferred upon them their immortality. Divine power allowed the gods to intervene in mortal affairs in various ways: they could cause natural events such as rain, wind, the growing of crops, or epidemics, and were able to dicta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fire (classical Element)
Fire is one of the four classical elements along with earth, water and air in ancient Greek philosophy and science. Fire is considered to be both hot and dry and, according to Plato, is associated with the tetrahedron. Greek and Roman tradition Fire is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with the qualities of energy, assertiveness, and passion. In one Greek myth, Prometheus stole ''fire'' from the gods to protect the otherwise helpless humans, but was punished for this charity. Fire was one of many '' archai'' proposed by the pre-Socratics, most of whom sought to reduce the cosmos, or its creation, to a single substance. Heraclitus considered ''fire'' to be the most fundamental of all elements. He believed fire gave rise to the other three elements: "All things are an interchange for fire, and fire for all things, just like goods for gold and gold for goods." Diels-Kranz B90 (Freeman 9481970p. 45. He had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), 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 education, mathematics teacher to higher level students, one of whom was named Hermodorus.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) 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. Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drown
Drowning is a type of suffocation induced by the submersion of the mouth and nose in a liquid. Submersion injury refers to both drowning and near-miss incidents. Most instances of fatal drowning occur alone or in situations where others present are either unaware of the victim's situation or unable to offer assistance. After successful resuscitation, drowning victims may experience breathing problems, confusion, or unconsciousness. Occasionally, victims may not begin experiencing these symptoms until several hours after they are rescued. An incident of drowning can also cause further complications for victims due to low body temperature, aspiration, or acute respiratory distress syndrome (respiratory failure from lung inflammation). Drowning is more likely to happen when spending extended periods of time near large bodies of water. Risk factors for drowning include alcohol use, drug use, epilepsy, minimal swim training or a complete lack of training, and, in the case of child ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bronze
Bronze is an alloy consisting primarily of copper, commonly with about 12–12.5% tin and often with the addition of other metals (including aluminium, manganese, nickel, or zinc) and sometimes non-metals (such as phosphorus) or metalloids (such as arsenic or silicon). These additions produce a range of alloys some of which are harder than copper alone or have other useful properties, such as strength, ductility, or machinability. The archaeological period during which bronze was the hardest metal in widespread use is known as the Bronze Age. The beginning of the Bronze Age in western Eurasia is conventionally dated to the mid-4th millennium BCE (~3500 BCE), and to the early 2nd millennium BCE in China; elsewhere it gradually spread across regions. The Bronze Age was followed by the Iron Age, which started about 1300 BCE and reaching most of Eurasia by about 500 BCE, although bronze continued to be much more widely used than it is in modern times. Because historica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
