Square - Coordinates and Equations

Coordinates and Equations

The coordinates for the vertices of a square centered at the origin and with side length 2 are (±1, ±1), while the interior of the same consists of all points (x_i, y_i) with −1 < x_i < 1 and −1 < y_i < 1.

The equation

describes a square of side 2, centered at the origin. This equation means "x2 or y2, whichever is larger, equals 1." The circumradius of this square (the radius of a circle drawn through the square's vertices) is half the square's diagonal, and equals . Then the circumcircle has the equation