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Archimedean Academy
Archimedean means of or pertaining to or named in honor of the Greek mathematician Archimedes and may refer to: Mathematics *Archimedean absolute value *Archimedean circle *Archimedean constant *Archimedean copula *Archimedean field *Archimedean group *Archimedean point *Archimedean property *Archimedean solid *Archimedean spiral *Archimedean tiling Other uses *Archimedean screw *Claw of Archimedes *The Archimedeans, the mathematical society of the University of Cambridge *Archimedean Dynasty ''Archimedean Dynasty'' (German: ''Schleichfahrt'', meaning silent running) was the first of the ''AquaNox'' series of computer games, developed by Massive Development and published by Blue Byte in 1996. On July 29, 2015, after years of non-ava ... * Archimedean Upper Conservatory See also * Archimedes (other) * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,* * * * * * * * * * Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Heath, Thomas L. 1897. ''Works of Archimedes''. Archimedes' other mathematical achievements include deriving an approximation of pi, defining and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Absolute Value
In algebra, an absolute value (also called a valuation, magnitude, or norm, although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if ''D'' is an integral domain, then an absolute value is any mapping , x, from ''D'' to the real numbers R satisfying: It follows from these axioms that , 1, = 1 and , -1, = 1. Furthermore, for every positive integer ''n'', :, ''n'', = , 1 + 1 + ... + 1 (''n'' times), = , −1 − 1 − ... − 1 (''n'' times), ≤ ''n''. The classical " absolute value" is one in which, for example, , 2, =2, but many other functions fulfill the requirements stated above, for instance the square root of the classical absolute value (but not the square thereof). An absolute value induces a metric (and thus a topology) by d(f,g) = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Circle
In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and ''r'' denotes the radiius of any of the inner half circles, then the radius ''ρ'' of such an Archimedean circle is given by :\rho=\fracr\left(1-r\right), There are over fifty different known ways to construct Archimedean circles. Origin An Archimedean circle was first constructed by Archimedes in his ''Book of Lemmas''. In his book, he constructed what is now known as Archimedes' twin circles. Radius If a and b are the radii of the small semicircles of the arbelos, the radius of an Archimedean circle is equal to :R = \frac This radius is thus \frac 1R = \frac 1a + \frac 1b. The Archimedean circle with center C (as in the figure at right) is tangent to the tangents from the centers of the small semicircles to the other small semicir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Constant
The number (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of , sometimes by computing i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Copula
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval , 1 Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications. Sklar's theorem states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables. Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulae ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Field
In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. The property, typically construed, states that given two positive numbers ''x'' and ''y'', there is an integer ''n'' such that ''nx'' > ''y''. It also means that the set of natural numbers is not bounded above. Roughly speaking, it is the property of having no ''infinitely large'' or ''infinitely small'' elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ ''On the Sphere and Cylinder''. The notion arose from the theory of magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are ''comparable' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Group
In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes. Definition An additive group consists of a set of elements, an associative addition operation that combines pairs of elements and returns a single element, an identity element (or zero element) whose sum with any other element is the other element, and an additive inverse operation such that the sum of any element and its inverse is zero. A group is a linearly ordered group when, in addition, its ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Point
An Archimedean point () is a hypothetical viewpoint from which certain objective truths can perfectly be perceived (also known as a God's-eye view) or a reliable starting point from which one may reason. In other words, a view from an Archimedean point describes the ideal of removing oneself from the object of study so that one can see it in relation to all other things while remaining independent of them. For example, the philosopher John Rawls uses the heuristic device of the original position in an attempt to remove the particular biases of individual agents to demonstrate how rational beings might arrive at an objective formulation of justice. Origins The term refers to the great mathematician Archimedes, who supposedly claimed that he could lift the Earth off its foundation if he were given a place to stand, one solid point, and a long enough lever. The idea for the term is attributed to Descartes in his second ''Meditation'', who refers to Archimedes requiring only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Property
In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. The property, typically construed, states that given two positive numbers ''x'' and ''y'', there is an integer ''n'' such that ''nx'' > ''y''. It also means that the set of natural numbers is not bounded above. Roughly speaking, it is the property of having no ''infinitely large'' or ''infinitely small'' elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ ''On the Sphere and Cylinder''. The notion arose from the theory of magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are ''comparabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed of only one type of polygon), excluding the prisms and antiprisms, and excluding the pseudorhombicuboctahedron. They are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices. "Identical vertices" means that each two vertices are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid directly on its initial position. observed that a 14th polyhedron, the elongated square gyrobicupola (or pseudo-rhombicuboctahedron), meets a weaker definition of an Archimedean solid, in which "identical vertices" means merely that the faces surrounding each vertex are of the same types (i.e. each vertex looks the same from close up), so only a lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Spiral
The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates it can be described by the equation r = a + b\cdot\theta with real numbers and . Changing the parameter moves the centerpoint of the spiral outward from the origin (positive toward and negative toward ) essentially through a rotation of the spiral, while controls the distance between loops. From the above equation, it can thus be stated: position of particle from point of start is proportional to angle as time elapses. Archimedes described such a spiral in his book '' On Spirals''. Conon of Samos was a friend of his and Pappus states that this spiral was discovered by Conon. Derivation of general equation of spiral A p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Tiling
Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler in his ''Harmonices Mundi'' (Latin: ''The Harmony of the World'', 1619). Notation of Euclidean tilings Euclidean tilings are usually named after Cundy & Rollett’s notation. This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 36; 36; 34.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 36; 36 (both of different transitivity class), or (36)2, tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided polygons (triangles). With a final vertex 34.6, 4 more contiguous equilateral triangles and a single regular hexagon. However, this notation has two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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