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In geometry, a square is ( also outdated em ) a special polygon, ie a planar, convex and regular quadrangle.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.