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The geometric mean is defined as the n th root of the product of n numbers, i.e., for a collection of numbers a1, a2, ..., an, the geometric mean is defined as. or, equivalently, as the arithmetic mean in logarithmic scale: The geometric mean of two numbers, say 2 and 8, is the square root of their product, that is, .
Main article: Arithmetic mean. The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample , usually denoted by , is the sum of the sampled values divided by the number of items in the sample. For example, the arithmetic mean of five values: 4, 36 ...
Geometric mean theorem. In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of those two segments equals the altitude.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had ...
The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest. If the data set has an odd number of observations, the middle one is selected (after arranging in ascending order). For example, the following list of seven numbers, 1, 3, 3, 6, 7, 8, 9.
projection. A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, R 2 → R , ( x , y ) ↦ x {\displaystyle \mathbb {R} ^ {2}\to \mathbb {R} , (x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection.
In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as times of day, and fractional parts of real numbers. This is necessary since most of the usual means may not be appropriate on angle-like quantities. For example, the arithmetic mean of 0° and 360° is 180°, which ...
Geometry of numbers. Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattices provides fundamental information on algebraic numbers. [1] Hermann Minkowski (1896) initiated this line of research at the ...
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