sumsquare

Sumsquare is a term used in mathematics to describe the operation of adding together the squares of numbers, vectors, or components. The basic form is the sum of squares of integers 1 through n: 1^2+2^2+...+n^2 = n(n+1)(2n+1)/6. In vector spaces, the squared Euclidean norm of a vector x = (x1,...,xk) is defined as ||x||^2 = x1^2+...+xk^2.

In number theory, sums of squares refers to representations of integers as sums of squares, such as expressing a number as a^2+b^2. The two-squares theorem characterizes primes that are sums of two squares: a prime p equals a^2+b^2 with integers a,b if and only if p=2 or p ≡ 1 (mod 4). Lagrange's four-square theorem states that every natural number can be written as a sum of four squares. The study of sums of squares connects to quadratic forms and modular arithmetic.

In computing and data analysis, the term may appear as shorthand in algorithms involving squared errors, least-squares optimization, or norm calculations. Software libraries and programming projects sometimes adopt the name SumSquare or sumsquare for modules dealing with numerical computation, statistics, or data processing. The exact meaning depends on context, but the underlying concept is consistent with summing squared quantities.