Neliöittäminen

Neliöittäminen is the Finnish term for squaring, a mathematical operation that multiplies a number by itself. The word derives from the root neliö, meaning square, combined with the infinitive suffix –ttäm. Squaring a real or complex number x yields x². The result is always non‑negative for real x and has the same sign as x for integer powers beyond sign reversal.

The operation is central in algebraic identities such as (a+b)² = a²+2ab+b² and (a−b)² = a²−2ab+b², used in solving quadratic equations. Geometrically, squaring corresponds to determining the area of a square with side length x. In analytic geometry, the square of a distance between points leads to the Euclidean norm squared.

In number theory, perfect squares are integers that are squares of integers; 1, 4, 9, 16… exhibit properties such as being congruent to 0 or 1 modulo 4. Squares also appear in Pythagorean triples, where the sum of squares of two legs equals the square of the hypotenuse.

Computationally, squaring is an elementary operation in algorithms, being used in cryptography (e.g., modular exponentiation), graphics (pixel intensity), and statistical calculations (variance computation).