Sum of squares

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In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts:

Number theory
Algebra and algebraic geometry
Euclidean geometry and other inner-product spaces
  • 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.
  • 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)
  • The British flag theorem for rectangles equates two sums of two squares
  • The parallelogram law equates the sum of the squares of the four sides to the sum of the squares of the diagonals

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