The squaring operation defines a real function called the square function or the squaring function. Its domain is the whole
The … See more

There are several major uses of the square function in geometry.
The name of the square function shows its importance in the definition of the area: it comes from the fact that the area of a square with … See more

The square function is defined in any field or ring. An element in the image of this function is called a square, and the inverse images of a square are called square roots.
The notion of squaring is particularly important i… See more

On complex numbers, the square function is a twofold cover in the sense that each non-zero complex number has exactly two square roots.
The square of the absolute value of a complex nu… See more

Squares are ubiquitous in algebra, more generally, in almost every branch of mathematics, and also in physics where many units are defined using squares and inverse squares: see below.
Least squa… See more

• Exponentiation by squaring
• Polynomial SOS, the representation of a non-negative polynomial as the sum of squares of polynomials
• Hilbert's seventeenth problem, for the representation of positive polynomials as … See more

• Marshall, Murray Positive polynomials and sums of squares. Mathematical Surveys and Monographs, 146. American Mathematical Society, Providence, RI, 2008. xii+187 pp. ISBN 978-0-8218-4402-1, ISBN… See more