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| In [[mathematics]], [[statistics]] and elsewhere, '''sums of squares''' occur in a number of contexts:
| | Pig Farmer Loren from Cold Lake, has hobbies and interests including cycling, opal and bottle tops collecting. In the previous year has completed a journey to German Nazi Concentration and Extermination Camp (-).<br><br>Here is my web page: [http://www.comoganhardinheiro101.com/perguntas-frequentes/ como ganhar dinheiro na internet] |
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| ;Statistics
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| * For partitioning of variance, see [[Partition of sums of squares]]
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| * For the "sum of squared deviations", see [[Least squares]]
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| * For the "sum of squared differences", see [[Mean squared error]]
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| * For the "sum of squared error", see [[Residual sum of squares]]
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| * For the "sum of squares due to lack of fit", see [[Lack-of-fit sum of squares]]
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| * For sums of squares relating to model predictions, see [[Explained sum of squares]]
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| * For sums of squares relating to observations, see [[Total sum of squares]]
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| * For sums of squared deviations, see [[Squared deviations]]
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| * For modelling involving sums of squares, see [[Analysis of variance]]
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| * For modelling involving the multivariate generalisation of sums of squares, see [[Multivariate analysis of variance]]
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| ;Number theory
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| * For the sum of squares of consecutive integers, see [[Square pyramidal number]]
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| * For representing an integer as a sum of squares of 4 integers, see [[Lagrange's four-square theorem]]
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| * [[Descartes' theorem]] for four kissing circles involves sums of squares
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| * [[Fermat's theorem on sums of two squares]] says which integers are sums of two squares.
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| ** A separate article discusses [[Proofs of Fermat's theorem on sums of two squares]]
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| * [[Pythagorean triple]]s are sets of three integers such that the sum of the squares of the first two equals the square of the third.
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| * [[Integer triangle#Pythagorean triangles with integer altitude from the hypotenuse|Pythagorean triangles with integer altitude from the hypotenuse]] have the sum of squares of inverses of the integer legs equal to the square of the inverse of the integer altitude from the hypotenuse.
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| * [[Pythagorean quadruple]]s are sets of four integers such that the sum of the squares of the first three equals the square of the fourth.
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| * The [[Basel problem]], solved by Euler in terms of <math>\pi</math>, asked for an exact expression for the sum of the squares of the reciprocals of all positive integers.
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| * [[Rational Trigonometry]]'s triple-quad rule and triple-spread rule contains sums of squares. (similar to Heron's formula)
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| ;Algebra and algebraic geometry
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| * For representing a polynomial as the sum of squares of ''polynomials'', see [[Polynomial SOS]].
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| ** For ''computational optimization'', see [[Sum-of-squares optimization]].
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| * For representing a multivariate polynomial that takes only non-negative values over the reals as a sum of squares of ''rational functions'', see [[Hilbert's seventeenth problem]].
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| * The [[Brahmagupta–Fibonacci identity]] says the set of all sums of two squares is closed under multiplication.
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| ;Euclidean geometry and other inner-product spaces
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| * The [[Pythagorean theorem]] says that the square on the hypotenuse of a right triangle is equal in area to the sum of the squares on the legs.
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| * [[Heron's formula]] for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares)
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| * The [[British flag theorem]] for rectangles equates two sums of two squares
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| ==See also==
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| *[[Sums of powers]]
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| {{mathdab}}
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Pig Farmer Loren from Cold Lake, has hobbies and interests including cycling, opal and bottle tops collecting. In the previous year has completed a journey to German Nazi Concentration and Extermination Camp (-).
Here is my web page: como ganhar dinheiro na internet