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Quadrature Of The Parabola
''Quadrature of the Parabola'' () is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line (geometry), line) is \tfrac43 that of a certain inscribed triangle. It is one of the best-known works of Archimedes, in particular for its ingenious use of the method of exhaustion and in the second part of a geometric series. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He then computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of a ''reductio ad absurdum'' argument in ancient Greek mathematics, and Archimedes' solution remained unsurpassed until the development of integral calculus in the 17th centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Segment
Parabolic usually refers to something in a shape of a parabola, but may also refer to a parable. Parabolic may refer to: *In mathematics: **In elementary mathematics, especially elementary geometry: **Parabolic coordinates **Parabolic cylindrical coordinates **Möbius transformation#Parabolic transforms, parabolic Möbius transformation **Parabolic geometry (other) **Fermat's spiral, Parabolic spiral **Parabolic line **In advanced mathematics: ***Parabolic cylinder function ***Parabolic induction ***Parabolic Lie algebra ***Parabolic partial differential equation *In physics: **Parabolic trajectory *In technology: **Parabolic antenna **Parabolic microphone **Parabolic reflector **Parabolic trough - a type of solar thermal energy collector **Parabolic flight - a way of achieving weightlessness **Fishing rod#Specifications, Parabolic action, or parabolic bending curve - a term often used to refer to a progressive bending curve in fishing rods. *In commodities and stock market ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Sections
A conic section, conic or a quadratic curve is a curve obtained from a Conical surface, cone's surface intersecting a plane (mathematics), plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The Greek mathematics, ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set (mathematics), set of those points whose distances to some particular point, called a ''Focus (geometry), focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''Eccentricity (mathematics), eccentricity''. The type of conic is determined by the value of the ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Sum
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance. Among the Ancient Greeks, the idea that a potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit during the 17th century, especially through the early calculus of Isaac Newton. The re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrature Parabola Relative Sizes
Quadrature may refer to: Mathematics * Quadrature (geometry), drawing a square with the same area as a given plane figure (''squaring'') or computing that area ** Quadrature of the circle ** ''Quadrature of the Parabola'' ** Quadrature of the hyperbola * Numerical integration is often called "numerical quadrature" or simply "quadrature" ** Gaussian quadrature, a special case of numerical integration * Quadrature (differential equations), expressing a differential equation solution in terms of integrals. * Formerly, a synonym for "integral" ** Integral ** Antiderivative Signal processing * Addition in quadrature, combining the magnitude of uncorrelated signals by taking the square root of the sum of their squares *Quadrature phase, oscillations that are said to be ''in quadrature'' if they are separated in phase by 90° (/2, or /4) *Quadrature component of a composite signal *Quadrature filter, the analytic signal of a real-valued filter *Quadrature amplitude modulation (QAM) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, Aerospace engineering, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including Algebraic geometry, algebraic, Differential geometry, differential, Discrete geometry, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Segment Dissection
Parabolic usually refers to something in a shape of a parabola, but may also refer to a parable. Parabolic may refer to: *In mathematics: **In elementary mathematics, especially elementary geometry: **Parabolic coordinates **Parabolic cylindrical coordinates ** parabolic Möbius transformation ** Parabolic geometry (other) ** Parabolic spiral ** Parabolic line **In advanced mathematics: *** Parabolic cylinder function ***Parabolic induction ***Parabolic Lie algebra ***Parabolic partial differential equation *In physics: **Parabolic trajectory *In technology: **Parabolic antenna **Parabolic microphone **Parabolic reflector **Parabolic trough - a type of solar thermal energy collector **Parabolic flight - a way of achieving weightlessness ** Parabolic action, or parabolic bending curve - a term often used to refer to a progressive bending curve in fishing rods. *In commodities and stock markets: ** Parabolic SAR - a chart pattern in which prices rise or fall with an increasin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Sections
A conic section, conic or a quadratic curve is a curve obtained from a Conical surface, cone's surface intersecting a plane (mathematics), plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The Greek mathematics, ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set (mathematics), set of those points whose distances to some particular point, called a ''Focus (geometry), focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''Eccentricity (mathematics), eccentricity''. The type of conic is determined by the value of the ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On The Equilibrium Of Planes
On, on, or ON may refer to: Arts and entertainment Music * On (band), a solo project of Ken Andrews * ''On'' (EP), a 1993 EP by Aphex Twin * ''On'' (Echobelly album), 1995 * ''On'' (Gary Glitter album), 2001 * ''On'' (Imperial Teen album), 2002 * ''On'' (Elisa album), 2006 * ''On'' (Jean album), 2006 * ''On'' (Boom Boom Satellites album), 2006 * ''On'' (Tau album), 2017 * "On" (song), a 2020 song by BTS * "On", a song by Bloc Party from the 2006 album '' A Weekend in the City'' * "On", a song by Anson Lo, 2023 Other media * '' Ön'', a 1966 Swedish film * On (Japanese prosody), the counting of sound units in Japanese poetry * ''On'' (novel), by Adam Roberts * ONdigital, a failed British digital television service, later called ITV Digital * Overmyer Network, a former US television network Places * On (Ancient Egypt), a Hebrew form of the ancient Egyptian name of Heliopolis * On, Wallonia, a district of the municipality of Marche-en-Famenne * Ahn, Luxembourg, know ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lever
A lever is a simple machine consisting of a beam (structure), beam or rigid rod pivoted at a fixed hinge, or '':wikt:fulcrum, fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load, and effort, the lever is divided into Lever#Types of levers, three types. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage, which is mechanical advantage gained in the system, equal to the ratio of the output force to the input force. As such, the lever is a mechanical advantage device, trading off force against movement. Etymology The word "lever" entered English language, English around 1300 from . This sprang from the stem of the verb ''lever'', meaning "to raise". The verb, in turn, goes back to , itself from the adjective ''levis'', meaning "light" (as in "not heavy"). The word's primary origin is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
