**A square** is a regular quadrilateral , that is, a quadrilateral in which all angles are equal and all sides are equal. A square is at the same time a special case of a rhombus and a rectangle .

Square | |
---|---|

Ribs | four |

Shlefly Symbol | {four} |

Type of symmetry | Dihedral group (D _{4} ) |

Square | t ^{2} |

Inside corner | 90 ° |

## Square Properties

- The lengths of all sides are equal.
- All corners of the square are straight.
- The diagonals of a square are equal, mutually perpendicular, the intersection point is divided in half and are bisectors of angles.

## Properties

- Let be$t$ - side of a square,$R$ - radius of the circumscribed circle ,$r$ - radius of the inscribed circle . Then the center of the circumscribed and inscribed circles of the square coincides with the intersection point of its diagonals, and
- the radius of the inscribed circle of the square is equal to half the side of the square:
- $r=\frac{t}{2}$ ,

- the radius of the circumscribed circle of the square is equal to half the diagonal of the square:
- $R=\frac{\sqrt{2}}{2}t$ ,

- the radius of the inscribed circle of the square is equal to half the side of the square:
- A square has the greatest symmetry among all quadrangles. He has:
- one axis of symmetry of the fourth order (the axis perpendicular to the plane of the square and passing through its center);
- four axes of symmetry of the second order (which for a flat figure is equivalent to reflections), of which two pass along the diagonals of the square, and the other two parallel to the sides.

- The diagonals of the square are equal, mutually perpendicular, the intersection point is divided in half and divide the corners of the square in half.

## Square Perimeter

- the perimeter of the square is:
- $P=\mathrm{four}t=\mathrm{four}\sqrt{2}R=\mathrm{eight}r$ ,

- the perimeter of the square is:

## Square Area

*Here are formulas that are specific to a square.**See also formulas for the area of arbitrary quadrangles .*

- square$S$ square equal
- $S={t}^{2}=2{R}^{2}=\mathrm{four}{r}^{2}$ .

- square$S$ square equal

## Non-Euclidean geometry

In non-Euclidean geometry, a square (more broadly) is a polygon with four equal sides and equal angles.

## Variety of Squares

The squares are the faces of the cube - one of the five regular polyhedra .

Graphs: K _{4 a} complete graph is often depicted as a square with six edges.

3- simplex (3D) |

A chessboard has the shape of a square and is divided into 64 squares of two colors. The square board for international drafts is divided into 100 squares of two colors. The boxing ring and the square are square .

The square flag of Lima is divided into two black and two yellow squares, being raised on a ship in the harbor , means that the ship is in quarantine .

## See also

- The square is called exponentiation 2
- Circle squared
- Unit square
- Squaring a square
- Parallelogram of Varignon
- Thebo Theorem 1
- Quadrangle
- Marching squares

## Links

- A square, a geometric figure // Brockhaus and Efron Encyclopedic Dictionary : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.