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Witch Of Agnesi
In mathematics, the witch of Agnesi () is a cubic plane curve defined from two diametrically opposite points of a circle. It gets its name from Italian mathematician Maria Gaetana Agnesi, and from a mistranslation of an Italian word for a sailing sheet. Before Agnesi, the same curve was studied by Fermat, Grandi, and Newton. The graph of the derivative of the arctangent function forms an example of the witch of Agnesi. As the probability density function of the Cauchy distribution, the witch of Agnesi has applications in probability theory. It also gives rise to Runge's phenomenon in the approximation of functions by polynomials, has been used to approximate the energy distribution of spectral lines, and models the shape of hills. The witch is tangent to its defining circle at one of the two defining points, and asymptotic to the tangent line to the circle at the other point. It has a unique vertex (a point of extreme curvature) at the point of tangency with its defining c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witch Of Agnesi Curves
Witchcraft traditionally means the use of magic or supernatural powers to harm others. A practitioner is a witch. In medieval and early modern Europe, where the term originated, accused witches were usually women who were believed to have used malevolent magic against their own community, and often to have communed with evil beings. It was thought witchcraft could be thwarted by protective magic or counter-magic, which could be provided by cunning folk or folk healers. Suspected witches were also intimidated, banished, attacked or killed. Often they would be formally prosecuted and punished, if found guilty or simply believed to be guilty. European witch-hunts and witch trials in the early modern period led to tens of thousands of executions. In some regions, many of those accused of witchcraft were folk healers or midwives. European belief in witchcraft gradually dwindled during and after the Age of Enlightenment. Contemporary cultures that believe in magic and the super ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex (curve)
In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature. However, other special cases may occur, for instance when the second derivative is also zero, or when the curvature is constant. For space curves, on the other hand, a vertex is a point where the torsion vanishes. Examples A hyperbola has two vertices, one on each branch; they are the closest of any two points lying on opposite branches of the hyperbola, and they lie on the principal axis. On a parabola, the sole vertex lies on the axis of symmetry and in a quadratic of the form: :ax^2 + bx + c\,\! it can be found by completing the square or by differentiation., p. 127. On an ellipse, two of the four vertices lie on the major axis and two lie on the minor axis. For a circle, which has constant curvature, every point is a verte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Of Revolution
In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the ''axis of revolution'') that lies on the same plane. The surface created by this revolution and which bounds the solid is the surface of revolution. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area ( Pappus's second centroid theorem). A representative disc is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length ) around some axis (located units away), so that a cylindrical volume of units is enclosed. Finding the volume Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration. To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Calculus
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. For example, the equations :\begin x &= \cos t \\ y &= \sin t \end form a parametric representation of the unit circle, where ''t'' is the parameter: A point (''x'', ''y'') is on the unit circle if and only if there is a value of ''t'' such that these two equations generate that point. Sometimes the parametric equations for the individual scalar output variables are combined into a single parametric equation in vectors: :(x, y)=(\cos t, \sin t). Parametric representations are generally nonunique (see the "Examples in two dimensions" section bel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the deriva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation'' refers only to ''univariate equations'', that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the ''multivariate'' case), the term ''polynomial equation'' is usually preferred to ''algebraic equation''. For example, :x^5-3x+1=0 is an algebraic equation with integer coefficients and :y^4 + \frac - \frac + xy^2 + y^2 + \frac = 0 is a multivariate polynomial equation over the rationals. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clearing Denominators
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions. Example Consider the equation : \frac x 6 + \frac y = 1. The smallest common multiple of the two denominators 6 and 15''z'' is 30''z'', so one multiplies both sides by 30''z'': : 5xz + 2y = 30z. \, The result is an equation with no fractions. The simplified equation is not entirely equivalent to the original. For when we substitute and in the last equation, both sides simplify to 0, so we get , a mathematical truth. But the same substitution applied to the original equation results in , which is mathematically meaningless. Description Without loss of generality, we may assume that the right-hand side of the equation is 0, since an equation may equivalently be rewritten in the form . So let the equation have the form :\sum_^n \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Origin (mathematics)
In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter ''O'', used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same answer. This allows one to pick an origin point that makes the mathematics as simple as possible, often by taking advantage of some kind of geometric symmetry. Cartesian coordinates In a Cartesian coordinate system, the origin is the point where the axes of the system intersect.. The origin divides each of these axes into two halves, a positive and a negative semiaxis. Points can then be located with reference to the origin by giving their numerical coordinates—that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secant Line
Secant is a term in mathematics derived from the Latin ''secare'' ("to cut"). It may refer to: * a secant line, in geometry * the secant variety, in algebraic geometry * secant (trigonometry) (Latin: secans), the multiplicative inverse (or reciprocal) trigonometric function of the cosine * the secant method, a root-finding algorithm in numerical analysis, based on secant lines to graphs of functions * a secant ogive Secant is a term in mathematics derived from the Latin ''secare'' ("to cut"). It may refer to: * a secant line, in geometry * the secant variety, in algebraic geometry * secant (trigonometry) (Latin: secans), the multiplicative inverse (or reciproc ... in nose cone design {{mathdab sr:Секанс ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agnesi
Agnesi is an Italian surname. Notable people with the surname include: * Alberto Agnesi (born 1980), Mexican telenovela actor * Luigi Agnesi (1833–1875), Belgian operatic bass-baritone, conductor and composer * Maria Gaetana Agnesi (1718–1799), Italian linguist, mathematician and philosopher; sister of Maria Teresa * Maria Teresa Agnesi Pinottini (1720–1795), Italian composer; sister of Maria Gaetana * Nicolas Agnesi (born 1988), French rugby player * Troilo Agnesi, 15th-century Roman Catholic prelate See also *Witch of Agnesi In mathematics, the witch of Agnesi () is a cubic plane curve defined from two diametrically opposite points of a circle. It gets its name from Italian mathematician Maria Gaetana Agnesi, and from a mistranslation of an Italian word for a sail ..., mathematical curve named after Maria Gaetana (also known as Agnesi witch) * 16765 Agnesi, asteroid, named for Maria Gaetana * Agnesi (crater), on planet Venus, named for Maria Gaetana {{surname, Ag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witch Of Agnesi, Construction
Witchcraft traditionally means the use of magic or supernatural powers to harm others. A practitioner is a witch. In medieval and early modern Europe, where the term originated, accused witches were usually women who were believed to have used malevolent magic against their own community, and often to have communed with evil beings. It was thought witchcraft could be thwarted by protective magic or counter-magic, which could be provided by cunning folk or folk healers. Suspected witches were also intimidated, banished, attacked or killed. Often they would be formally prosecuted and punished, if found guilty or simply believed to be guilty. European witch-hunts and witch trials in the early modern period led to tens of thousands of executions. In some regions, many of those accused of witchcraft were folk healers or midwives. European belief in witchcraft gradually dwindled during and after the Age of Enlightenment. Contemporary cultures that believe in magic and the super ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
