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The linear transformations T 1, T 2, and T 3 have a geometric interpretation in the language of quadratic forms. They are closely related to (but are not equal to) reflections generating the orthogonal group of x 2 + y 2 − z 2 over the integers.
Wikipedia Defenition In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [26] Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra.
The circle of radius with center at (,) in the – plane can be broken into two semicircles each of which is the graph of a function, + and , respectively: + = + (), = (), for values of ranging from to + .
The Italian statistician Corrado Gini developed the Gini coefficient and published it in his 1912 paper Variabilità e mutabilità (English: variability and mutability). [16] [17] Building on the work of American economist Max Lorenz, Gini proposed using the difference between the hypothetical straight line depicting perfect equality and the actual line depicting people's incomes as a measure ...
Graphene (/ ˈ ɡ r æ f iː n /) [1] is a carbon allotrope consisting of a single layer of atoms arranged in a honeycomb planar nanostructure. [2] [3] The name "graphene" is derived from "graphite" and the suffix -ene, indicating the presence of double bonds within the carbon structure.
A visual representation of the sampling process. In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population.
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