Arthur Laffer is best know for a curve that illustrates a theoretical relationship between what?
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Arthur Laffer Arthur Betz Laffer ( ; born August 14, 1940) is an American economist who first gained prominence during the Reagan administration as a member of Reagan's Economic Policy Advisory Board (1981–89). Laffer is best known for the Laffer curve, an illustration of the theory that there exists some tax rate between 0% and 100% that will result in maximum tax revenue for governments. He is the author and co-author of many books and newspaper articles, including "Supply Side Economics: Financial Decision-Making for the 80s". Laffer is Policy Co-Chairman (with Lawrence "Larry" Kudlow) of the Free Enterprise Fund and serves on the "Board of Scholars" of the American Legislative Exchange Council (ALEC). Mr Laffer was one of four economists who acted as advisors to Donald Trump's successful 2016 campaign for the presidency of the United States.
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Laffer curve In economics, the Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of government revenue. It illustrates the concept of taxable income elasticity—i.e., taxable income changes in response to changes in the rate of taxation. The Laffer curve assumes that no tax revenue is raised at the extreme tax rates of 0% and 100%, and that there is a rate between 0% and 100% that maximizes government taxation revenue. The Laffer curve is typically represented as a graph that starts at 0% tax with zero revenue, rises to a maximum rate of revenue at an intermediate rate of taxation, and then falls again to zero revenue at a 100% tax rate. However, the shape of the curve is uncertain and disputed among economists.
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Faber–Jackson relation The Faber–Jackson relation is an early empirical power-law relation between the luminosity formula_1 and the central stellar velocity dispersion formula_2 of elliptical galaxies, first noted by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976. The original relation can be expressed mathematically as:
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Jordan curve theorem In topology, a "Jordan curve" is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a "plane simple closed curve". The Jordan curve theorem asserts that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points, so that every continuous path connecting a point of one region to a point of the other intersects with that loop somewhere. While the statement of this theorem seems to be intuitively obvious, it takes quite a bit of ingenuity to prove it by elementary means. More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces.
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Playfair's law In estimating erosion, Playfair's law is an empirical relationship that relates the size of a stream to the valley it runs through. It is better defined as a theory rather than law.
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Yerkes–Dodson law The Yerkes–Dodson law is an empirical relationship between arousal and performance, originally developed by psychologists Robert M. Yerkes and John Dillingham Dodson in 1908. The law dictates that performance increases with physiological or mental arousal, but only up to a point. When levels of arousal become too high, performance decreases. The process is often illustrated graphically as a bell-shaped curve which increases and then decreases with higher levels of arousal.
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Pierre de Fermat Pierre de Fermat (] ; (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the "Parlement" of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' "Arithmetica".
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Gerhard Frey Gerhard Frey (] ; born 1944) is a German mathematician, known for his work in number theory. His Frey curve, a construction of an elliptic curve from a purported solution to the Fermat equation, was central to Wiles' proof of Fermat's Last Theorem.
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Cost curve In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms use these curves to find the optimal point of production (minimizing cost), and profit maximizing firms can use them to decide output quantities to achieve those aims. There are various types of cost curves, all related to each other, including total and average cost curves, and marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves. Some are applicable to the short run, others to the long run.
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Ernst Engel Ernst Engel (March 26, 1821 – December 8, 1896) was a German statistician and economist, famous for the Engel curve and the Engel's law.
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Edmond Laguerre Edmond Nicolas Laguerre (April 9, 1834, Bar-le-Duc – August 14, 1886, Bar-le-Duc) was a French mathematician, a member of the Académie française (1885). His main works were in the areas of geometry and complex analysis. He also investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials. He laid the foundations of a geometry of oriented spheres (Laguerre geometry and Laguerre plane), including the Laguerre transformation or transformation by reciprocal directions.
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Curve fitting Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.
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Z curve The Z curve (or Z-curve) method is a bioinformatics algorithm for genome analysis. The Z-curve is a three-dimensional curve that constitutes a unique representation of a DNA sequence, i.e., for the Z-curve and the given DNA sequence each can be uniquely reconstructed from the other.
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Sea-level curve The sea-level curve is the representation of the changes of the sea level throughout the geological history.
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Conchoid (mathematics) A conchoid is a curve derived from a fixed point "O", another curve, and a length "d". It was invented by the ancient Greek mathematician Nicomedes.
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Arrow of time The Arrow of Time, or Time's Arrow, is a concept developed in 1927 by the British astronomer Arthur Eddington involving the "one-way direction" or "asymmetry" of time. It is an unsolved general physics question. This direction, according to Eddington, can be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world (""a solid block of paper"").
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Clifford parallel In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The concept was first studied by William Kingdon Clifford in elliptic space. Since parallel lines have the property of equidistance, the term "parallel" was appropriated from Euclidean geometry, but in fact the "lines" of elliptic geometry are curves, and they have finite length, unlike the lines of Euclidean geometry. The algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit.
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Method of normals In calculus, the method of normals was a technique invented by Descartes for finding normal and tangent lines to curves. It represented one of the earliest methods for constructing tangents to curves. The method hinges on the observation that the radius of a circle is always normal to the circle itself. With this in mind Descartes would construct a circle that was tangent to a given curve. He could then use the radius at the point of intersection to find the slope of a normal line, and from this one can easily find the slope of a tangent line.
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Hjulström curve The Hjulström curve, named after Filip Hjulström (1902–1982), is a graph used by hydrologists and geologists to determine whether a river will erode, transport, or deposit sediment. It was originally published in his doctoral thesis "The River Fyris" in 1935. The graph takes sediment particle size and water velocity into account.
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Sigmoid function A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. Often, "sigmoid function" refers to the special case of the logistic function shown in the first figure and defined by the formula
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Limaçon trisectrix In geometry, a limaçon trisectrix (called simply a trisectrix by some authors) is a member of the limaçon family of curves which has the trisectrix, or angle trisection, property. It can be defined as locus of the point of intersection of two lines, each rotating at a uniform rate about separate points, so that the ratio of the rates of rotation is 2:3 and the lines initially coincide with the line between the two points. Thus, it is an example of a sectrix of Maclaurin.
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Connection (mathematics) In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a "parallel" and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields: the infinitesimal transport of a vector field in a given direction.