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Geometric mean

Index Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). [1]

64 relations: Anti-reflective coating, Arithmetic mean, Arithmetic underflow, Arithmetic–geometric mean, Aspect ratio (image), Average, Bolzano–Weierstrass theorem, CinemaScope, Compound annual growth rate, Conic section, Cube, Cube root, Cuboid, E (mathematical constant), Ellipse, Exponential growth, Focus (geometry), FT 30, Generalized mean, Geometric mean filter, Geometric mean theorem, Geometric standard deviation, Geometry, Harmonic mean, Heronian mean, Horizon, Human Development Index, Hyperbolic coordinates, Imaginary number, Inequality of arithmetic and geometric means, Instructions per cycle, Integer overflow, List of logarithmic identities, Log-normal distribution, Logarithm, Logarithmic mean, Mean, Mean-preserving spread, Muirhead's inequality, Multiplication, Multiplicative calculus, Nth root, Product (mathematics), Pythagorean means, Quadrature (mathematics), Quasi-arithmetic mean, Rate of return, Rectangle, Retail price index, Right triangle, ..., Root mean square, Semi-major and semi-minor axes, Sequence, Signal processing, Society of Motion Picture and Television Engineers, Spectral flatness, Sphere, Square, Square root, The Mathematical Gazette, United States congressional apportionment, Weighted geometric mean, World population, 14:9. Expand index (14 more) »

Anti-reflective coating

An antireflective or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses and other optical elements to reduce reflection.

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Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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Arithmetic underflow

The term arithmetic underflow (or "floating point underflow", or just "underflow") is a condition in a computer program where the result of a calculation is a number of smaller absolute value than the computer can actually represent in memory on its CPU.

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Arithmetic–geometric mean

In mathematics, the arithmetic–geometric mean (AGM) of two positive real numbers and is defined as follows: Call and and: \end Then define the two interdependent sequences and as \end where the square root takes the principal value.

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Aspect ratio (image)

The aspect ratio of an image describes the proportional relationship between its width and its height.

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Average

In colloquial language, an average is a middle or typical number of a list of numbers.

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Bolzano–Weierstrass theorem

In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rn.

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CinemaScope

CinemaScope is an anamorphic lens series used, from 1953 to 1967, for shooting widescreen movies.

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Compound annual growth rate

Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Cube root

In mathematics, a cube root of a number x is a number y such that y3.

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Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

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E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

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Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

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Focus (geometry)

In geometry, focuses or foci, singular focus, are special points with reference to which any of a variety of curves is constructed.

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FT 30

The FT 30 (FT Ordinary Index or FTOI, not "FTSE 30") is a now rarely used index that is similar to the Dow Jones Industrial Average.

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Generalized mean

In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).

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Geometric mean filter

The geometric mean filter is an image filtering process meant to smooth and reduce noise of an image.

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Geometric mean theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the lengths of the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.

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Geometric standard deviation

In probability theory and statistics, the geometric standard deviation describes how spread out are a set of numbers whose preferred average is the geometric mean.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

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Heronian mean

In mathematics, the Heronian mean H of two non-negative real numbers A and B is given by the formula: It is named after Hero of Alexandria.

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Horizon

The horizon or skyline is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not.

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Human Development Index

The Human Development Index (HDI) is a composite statistic (composite index) of life expectancy, education, and per capita income indicators, which are used to rank countries into four tiers of human development.

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Hyperbolic coordinates

In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane Hyperbolic coordinates take values in the hyperbolic plane defined as: These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion.

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Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

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Inequality of arithmetic and geometric means

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

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Instructions per cycle

In computer architecture, instructions per cycle (IPC) is one aspect of a processor's performance: the average number of instructions executed for each clock cycle.

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Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits – either larger than the maximum or lower than the minimum representable value.

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List of logarithmic identities

In mathematics, there are many logarithmic identities.

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Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logarithmic mean

In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient.

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Mean

In mathematics, mean has several different definitions depending on the context.

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Mean-preserving spread

In probability and statistics, a mean-preserving spread (MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A's probability density function or probability mass function while leaving the mean (the expected value) unchanged.

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Muirhead's inequality

In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Multiplicative calculus

In mathematics, a multiplicative calculus is a system with two multiplicative operators, called a "multiplicative derivative" and a "multiplicative integral", which are inversely related in a manner analogous to the inverse relationship between the derivative and integral in the classical calculus of Newton and Leibniz.

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Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

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Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

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Pythagorean means

In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM).

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Quadrature (mathematics)

In mathematics, quadrature is a historical term which means determining area.

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Quasi-arithmetic mean

In mathematics and statistics, the quasi-arithmetic mean or generalised f-mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function f. It is also called Kolmogorov mean after Russian mathematician Andrey Kolmogorov.

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Rate of return

In finance, return is a profit on an investment.

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Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

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Retail price index

In the United Kingdom, the retail prices index or retail price index (RPI) is a measure of inflation published monthly by the Office for National Statistics.

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Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

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Root mean square

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).

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Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

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Society of Motion Picture and Television Engineers

The Society of Motion Picture and Television Engineers (SMPTE) (rarely), founded in 1916 as the Society of Motion Picture Engineers or SMPE, is a global professional association, of engineers, technologists, and executives working in the media and entertainment industry.

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Spectral flatness

Spectral flatness or tonality coefficient, also known as Wiener entropy, is a measure used in digital signal processing to characterize an audio spectrum.

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Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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The Mathematical Gazette

The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.

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United States congressional apportionment

United States congressional apportionment is the process by which seats in the United States House of Representatives are distributed among the 50 states according to the most recent constitutionally mandated decennial census.

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Weighted geometric mean

In statistics, given a set of data, and corresponding weights, the weighted geometric mean is calculated as Note that if all the weights are equal, the weighted geometric mean is the same as the geometric mean.

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World population

In demographics, the world population is the total number of humans currently living, and was estimated to have reached 7.6 billion people as of May 2018.

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14:9

14:9 is a compromise aspect ratio of 1.56:1.

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Arithmetic harmonic mean, Arithmetic-harmonic mean, Arithmetic–harmonic mean, GEOMEAN, Geo mean, Geomean, Geometric Average, Geometric Mean, Geometric average, Geometrical Mean, Log average, Log-average.

References

[1] https://en.wikipedia.org/wiki/Geometric_mean

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