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Nicomedes (mathematician)
Nicomedes (; grc-gre, Νικομήδης; c. 280 – c. 210 BC) was an ancient Greek mathematician. Life and work Almost nothing is known about Nicomedes' life apart from references in his works. Studies have stated that Nicomedes was born in about 280 BC and died in about 210 BC. It is known that he lived around the time of Eratosthenes or after, because he criticized Eratosthenes' method of doubling the cube. It is also known that Apollonius of Perga called a curve of his creation a "sister of the conchoid", suggesting that he was naming it after Nicomedes' already famous curve. Consequently, it is believed that Nicomedes lived after Eratosthenes and before Apollonius of Perga. Like many geometers of the time, Nicomedes was engaged in trying to solve the problems of doubling the cube and trisecting the angle, both problems we now understand to be impossible using the tools of classical geometry. In the course of his investigations, Nicomedes created the conchoid of Nicom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conchoid Of Nicomedes
In geometry, a conchoid is a curve derived from a fixed point , another curve, and a length . It was invented by the ancient Greek mathematician Nicomedes. Description For every line through that intersects the given curve at the two points on the line which are from are on the conchoid. The conchoid is, therefore, the cissoid of the given curve and a circle of radius and center . They are called ''conchoids'' because the shape of their outer branches resembles conch shells. The simplest expression uses polar coordinates with at the origin. If :r=\alpha(\theta) expresses the given curve, then :r=\alpha(\theta)\pm d expresses the conchoid. If the curve is a line, then the conchoid is the ''conchoid of Nicomedes''. For instance, if the curve is the line , then the line's polar form is and therefore the conchoid can be expressed parametrically as :x=a \pm d \cos \theta,\, y=a \tan \theta \pm d \sin \theta. A limaçon is a conchoid with a circle as the given cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hippias
Hippias of Elis (; el, Ἱππίας ὁ Ἠλεῖος; late 5th century BC) was a Greek sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, and much else. Most of our knowledge of him is derived from Plato, who characterizes him as vain and arrogant. Life Hippias was born at Elis in the mid 5th-century BC (c. 460 BC) and was thus a younger contemporary of Protagoras and Socrates. He lived at least as late as Socrates (399 BC). He was a disciple of Hegesidamus. Owing to his talent and skill, his fellow-citizens availed themselves of his services in political matters, and in a diplomatic mission to Sparta. But he was in every respect like the other sophists of the time: he travelled about in various towns and districts of Greece for the purpose of teaching and public speaking. The two dialogues of Plato, the ''Hipp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
280s BC Births
8 (eight) is the natural number following 7 and preceding 9. In mathematics 8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of the form , being an integer greater than 1. * the first number which is neither prime nor semiprime. * the base of the octal number system, which is mostly used with computers. In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet. * a Fibonacci number, being plus . The next Fibonacci number is . 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube. * the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem. * the order of the smallest non-abelian group all of whose subgroups are normal. * the dimension of the octonions and is the highest possible dimension of a normed division algebra. * the first number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3rd-century BC Writers
The 3rd century was the period from 201 ( CCI) to 300 (CCC) Anno Domini (AD) or Common Era (CE) in the Julian calendar.. In this century, the Roman Empire saw a crisis, starting with the assassination of the Roman Emperor Severus Alexander in 235, plunging the empire into a period of economic troubles, barbarian incursions, political upheavals, civil wars, and the split of the Roman Empire through the Gallic Empire in the west and the Palmyrene Empire in the east, which all together threatened to destroy the Roman Empire in its entirety, but the reconquests of the seceded territories by Emperor Aurelian and the stabilization period under Emperor Diocletian due to the administrative strengthening of the empire caused an end to the crisis by 284. This crisis would also mark the beginning of Late Antiquity. In Persia, the Parthian Empire was succeeded by the Sassanid Empire in 224 after Ardashir I defeated and killed Artabanus V during the Battle of Hormozdgan. The Sassanids th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3rd-century BC Greek People
The 3rd century was the period from 201 ( CCI) to 300 (CCC) Anno Domini (AD) or Common Era (CE) in the Julian calendar.. In this century, the Roman Empire saw a crisis, starting with the assassination of the Roman Emperor Severus Alexander in 235, plunging the empire into a period of economic troubles, barbarian incursions, political upheavals, civil wars, and the split of the Roman Empire through the Gallic Empire in the west and the Palmyrene Empire in the east, which all together threatened to destroy the Roman Empire in its entirety, but the reconquests of the seceded territories by Emperor Aurelian and the stabilization period under Emperor Diocletian due to the administrative strengthening of the empire caused an end to the crisis by 284. This crisis would also mark the beginning of Late Antiquity. In Persia, the Parthian Empire was succeeded by the Sassanid Empire in 224 after Ardashir I defeated and killed Artabanus V during the Battle of Hormozdgan. The Sassanids t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Mathematicians
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eutocius
Eutocius of Ascalon (; el, Εὐτόκιος ὁ Ἀσκαλωνίτης; 480s – 520s) was a Palestinian-Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian ''Conics''. Life and work Little is known about the life of Eutocius. He was born in Ascalon, then in Palestina Prima. He lived during the reign of Justinian. Eutocius became head the school of philosophy in Athens following Ammonius and he was succeeded in this position by Olympiodorus, possibly as early as 525. He traveled to the greatest scientific centers of his time, including Alexandria, to conduct research on Archimedes' manuscripts. He wrote commentaries on Apollonius and on Archimedes. The surviving works of Eutocius are: *A Commentary on the first four books of the ''Conics'' of Apollonius. *Commentarieson: **the ''Sphere and Cylinder'' of Archimedes. **the ''Quadrature of the Circle'' of Archimedes (''In Archimedis circuli dimensionem'' in Latin). **the '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found. Despite the proof that it is impossible, attempts to square the circle have been common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratrix
In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and Ehrenfried Walther von Tschirnhaus, E. W. Tschirnhaus, which are both related to the circle. Quadratrix of Dinostratus The quadratrix of Dinostratus (also called the ''quadratrix of Hippias'') was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis. Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it effected a mechanical solution of squaring the circle. Pappus of Alexandria, Pappus, in his ''Collections'', treats its history, and gives two methods by which it can be generated. # Let a helix be drawn on a right circular cylinder (geometry), cylinder; a screw surface is then obtained by drawing line (geometry), lines from every point of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) ''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, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Context Pappus was active in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "How far he was above his contemporaries, how lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomedes , 94–74 BC
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Nicomedes may refer to: *Nicomedes (mathematician), ancient Greek mathematician who discovered the conchoid *Nicomedes of Sparta, regent during the youth of King Pleistoanax, commanded the Spartan army at the Battle of Tanagra (457 BC) *Saint Nicomedes, Martyr of unknown era, whose feast is observed 15 September Four kings of Bithynia in Anatolia, 3rd–1st century BC: *Nicomedes I of Bithynia, ruled 278–255 BC *Nicomedes II of Bithynia, 149–127 BC *Nicomedes III of Bithynia, 127–94 BC *Nicomedes IV of Bithynia Nicomedes IV Philopator ( grc-gre, Νικομήδης Φιλοπάτωρ) was the king of Bithynia from c. 94 BC to 74 BC. (''numbered as III. not IV.'') He was the first son and successor of Nicomedes III of Bithynia. Life Memnon of Heraclea wro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
