ruudu

Ruudu is the geometric figure known in English as a square. It is a regular quadrilateral with four equal sides and four right angles. Each interior angle measures 90 degrees, and opposite sides are parallel. The diagonals are equal in length, intersect at the center, bisect each other, and are perpendicular, dividing the square into four congruent right triangles.

If the side length is s, the area is s^2 and the perimeter is 4s. The diagonals have length s√2. In addition to these metric properties, a square has four lines of symmetry and rotational symmetry of order 4, belonging to the dihedral group D4.

In a coordinate plane, a standard square with side length s can be positioned with corners at (0,0), (s,0), (s,s), and (0,s); its center is at (s/2, s/2).

Ruudu appears in various mathematical contexts and everyday geometry. It is fundamental in tiling the plane, forming grid-based designs, pixel art, and architectural layouts. Board games and maps often use square grids for clear alignment and measurement, as seen on chessboards and checkerboards.

In Estonian usage, ruudu conveys the concept of a square, and related phrases describe attributes such as the area of a square. The term also appears in discussions of units of area and geometric figure references within mathematical and practical contexts.