In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles, π/2 radian angles, or See more

A quadrilateral is a square if and only if it is any one of the following:
• A rectangle with two adjacent equal sides.
• A rhombus with a right vertex angle. See more

The following animations show how to construct a square using a compass and straightedge. This is possible as 4 = 2 , a power of two. See more

Every acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so … See more

The coordinates for the vertices of a square with vertical and horizontal sides, centered at the origin and with side length 2 are (±1, ±1), while the … See more

The square has Dih4 symmetry, order 8. There are 2 dihedral subgroups: Dih2, Dih1, and 3 cyclic subgroups: Z4, Z2, and Z1. See more

Squaring the circle, proposed by ancient geometers, is the problem of constructing a square with the same area as a given circle, by using only a finite number of steps with compass and straightedge.
In 1882, the task was proven to be impossible as a … See more