|
In plane (Euclidean) geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides.
Classification A square is a special case of a regular quadrilateral, rectangle, rhombus, kite, parallelogram, and isosceles trapezoid/trapezium. Mensuration formulae The perimeter of a square whose sides have length s is And the area is In classical times, the second power was described in terms of the area of a square, as in the above formula. This led to the use of the term “square” to mean raising to the second power. Standard coordinates 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 (x0, x1) with −1 < xi < 1. Properties Each angle in a square is equal to 90 degrees, or a right angle. The diagonals of a square are equal. Conversely, if the diagonals of a rhombus are equal, then that rhombus must be a square. The diagonals of a square are (about 1.41) times the length of a side of the square. This value, known as Pythagoras’ constant, was the first number proven to be irrational. If a figure is both a rectangle and a rhombus then it is a square. Other facts Non-Euclidean geometry In non-euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles. In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger squares have smaller angles. Finite geometry In finite geometry, a subdivided p×p square, with p a prime number, provides a model for a finite geometry with p2 points. See finite geometry of the square and cube. See also | ||||||||
|
| |||||||||
 |
|
| |