Square

In geometry, a square is ( also outdated em ) a special polygon, ie a planar, convex and regular quadrangle. The square is a special case of the parallelogram and the trapezoid, it is both rectangle and rhombus ( diamond). For the construction of a square, an indication, such as the length of the side or the diagonal sufficient.

Squares are the boundary surfaces of the Platonic solids ( = three-dimensional regular polytopes ), namely the cube. The square is also a stone of a regular tiling. As a special case corresponding general n-dimensional body is both the square of the two-dimensional hypercube, as well as the two-dimensional cross-polytope.

Properties

For the square of the following applies:

• The four sides are the same length - it is equilateral.
• The four (interior) angles are equal - it is equiangular (all angles 90 °).
• It has four axes of symmetry: the two Seitensymmetralen ( perpendicular bisector ) and the two diagonals.
• It is 4- merous rotational symmetry and therefore point symmetry.
• The two diagonals are equal in length, bisect each other and are mutually perpendicular.
• The intersection of the diagonals is radius and incenter - the square is both tendon and tangent quadrilateral.
• The area of ​​the circumference is twice as large as that of the inscribed circle.

Formulary

Generalizations

The term square is generalized in synthetic geometry of the affine plane by a is the equivalent statements that describe a square in the elementary geometry used to define the concept. For example, the existence of these figures to an additional axiom for präeuklidische levels.