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Natural Logarithm
The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if the base is implicit, simply . Parentheses are sometimes added for clarity, giving , , or . This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity. The natural logarithm of is the exponentiation, power to which would have to be raised to equal . For example, is , because . The natural logarithm of itself, , is , because , while the natural logarithm of is , since . The natural logarithm can be defined for any positive real number as the Integral, area under the curve from to (with the area being negative when ). The simplicity of this definition, which is matched in many other formulas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities. For instance, the area of a square has a power law relationship with the length of its side, since if the length is doubled, the area is multiplied by 2, while if the length is tripled, the area is multiplied by 3, and so on. Empirical examples The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, cloud sizes, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Speidell
John Speidell (fl. 1600–1634) was an English mathematician. He is known for his early work on the calculation of logarithms. Speidell was a mathematics teacher in London and one of the early followers of the work John Napier had previously done on natural logarithms. In 1619 Speidell published a table entitled "New Logarithmes" in which he calculated the natural logarithms of sines, tangents, and secants. He then diverged from Napier's methods in order to ensure all of the logarithms were positive. A new edition of "New Logarithmes" was published in 1622 and contained an appendix with the natural logarithms of all numbers 1-1000. Along with William Oughtred and Richard Norwood, Speidell helped push toward the abbreviations of trigonometric functions. Speidel published a number of work about mathematics, including ''An Arithmeticall Extraction'' in 1628. His son, Euclid Speidell Euclid Speidell (died 1702) was an English customs official and mathematics teacher known for his wri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Mercator
Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician. He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he lived from 1642 to 1648 in the Netherlands. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). On 3 May 1661 he observed a transit of Mercury with Christiaan Huygens and Thomas Streete from Long Acre, London. On 14 November 1666 he was elected a Fellow of the Royal Society. He designed a marine chronometer for Charles II. In 1682 Jean Colbert invited Mercator to assist in the design and construction of the fountains at the Palace of Versailles, so he relocated there, but a falling-out with Colbert followed. Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Sector
A hyperbolic sector is a region (mathematics), region of the Cartesian plane bounded by a hyperbola and two ray (geometry), rays from the origin to it. For example, the two points and on the Hyperbola#Rectangular hyperbola, rectangular hyperbola , or the corresponding region when this hyperbola is re-scaled and its orientation (geometry), orientation is altered by a Rotation (geometry), rotation leaving the center at the origin, as with the Unit hyperbola#Parametrization, unit hyperbola. A hyperbolic sector in standard position has and . The argument of hyperbolic functions is the hyperbolic angle, which is defined as the area of a hyperbolic sector of the standard hyperbola ''xy'' = 1. This area is evaluated using natural logarithm. Hyperbolic triangle When in standard position, a hyperbolic sector determines a hyperbolic triangle, the right triangle with one vertex (geometry), vertex at the origin, base on the diagonal ray ''y'' = ''x'', and third vertex on the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbola
In mathematics, a hyperbola is a type of smooth function, smooth plane curve, curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected component (topology), connected components or branches, that are mirror images of each other and resemble two infinite bow (weapon), bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane (mathematics), plane and a double cone (geometry), cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Besides being a conic section, a hyperbola can arise as the locus (mathematics), locus of points whose difference of distances to two fixed focus (geometry), foci is constant, as a curve for each point of which the rays to two fix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrature (geometry)
In mathematics, quadrature is a historic term for the computation of area (mathematics), areas and is thus used for computation of integrals. The word is derived from the Latin ''quadratus'' meaning "square". The reason is that, for Ancient Greek mathematicians, the computation of an area consisted of constructing a square of the same area. In this sense, the modern term is squaring. For example, the quadrature of the circle, (or squaring the circle) is a famous old problem that has been shown, in the 19th century, to be impossible with the methods available to the Ancient Greeks, Integral calculus, introduced in the 17th century, is a general method for computation of areas. ''Quadrature'' came to refer to the computation of any integral; such a computation is presently called more often "integral" or "integration". However, the computation of solutions of differential equations and differential systems is also called ''integration'', and ''quadrature'' remains useful for dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historia Mathematica
''Historia Mathematica: International Journal of History of Mathematics'' is an academic journal on the history of mathematics published by Elsevier. It was established by Kenneth O. May in 1971 as the free newsletter ''Notae de Historia Mathematica'', but by its sixth issue in 1974 had turned into a full journal. The International Commission on the History of Mathematics began awarding the Montucla Prize, for the best article by an early career scholar in ''Historia Mathematica'', in 2009. The award is given every four years. Editors The editor in chief, editors of the journal have been: * Kenneth O. May (1974–1977) * Joseph Dauben, Joseph W. Dauben (1977–1985) * Eberhard Knobloch (1985–1994) * David E. Rowe (1994–1996) * Karen Hunger Parshall (1996–2000) * Craig Fraser and Umberto Bottazzini (2000–2004) * Craig Fraser (2004–2007) * Benno van Dalen (2007–2009) * June Barrow-Green and Niccolò Guicciardini (2010–2013) * Niccolò Guicciardini and Tom Archibald ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphonse Antonio De Sarasa
Alphonse Antonio de Sarasa, SJ was a Jesuit mathematician who contributed to the understanding of logarithms, particularly as areas under a hyperbola. Biography Alphonse de Sarasa was born in 1618, in Nieuwpoort in Flanders. In 1632 he was admitted as a novice in Ghent. It was there that he worked alongside Gregoire de Saint-Vincent whose ideas he developed, exploited, and promulgated. According to Sommervogel, Alphonse de Sarasa also held academic positions in Antwerp and Brussels. In 1649 Alphonse de Sarasa published ''Solutio problematis a R.P. Marino Mersenne Minimo propositi''. This book was in response to Marin Mersenne's pamphlet "Reflexiones Physico-mathematicae" which reviewed Saint-Vincent's ''Opus Geometricum'' and posed this challenge: : Given three arbitrary magnitudes, rational or irrational, and given the logarithms of the two, to find the logarithm of the third geometrically. R.P. BurnR. P. Burn (2001) "Alphonse Antonio de Sarasa and Logarithms", Historia M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
