Square - Other Facts

Other Facts

• The diagonals of a square are (about 1.414) times the length of a side of the square. This value, known as Pythagoras' constant, was the first number proven to be irrational.
• A square can also be defined as a parallelogram with equal diagonals that bisect the angles.
• If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then it is a square.
• If a circle is circumscribed around a square, the area of the circle is (about 1.571) times the area of the square.
• If a circle is inscribed in the square, the area of the circle is (about 0.7854) times the area of the square.
• A square has a larger area than any other quadrilateral with the same perimeter.
• A square tiling is one of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon).
• The square is in two families of polytopes in two dimensions: hypercube and the cross polytope. The Schläfli symbol for the square is {4}.
• The square is a highly symmetric object. There are four lines of reflectional symmetry and it has rotational symmetry of order 4 (through 90°, 180° and 270°). Its symmetry group is the dihedral group D₄.
• If the inscribed circle of a square ABCD has tangency points E on AB, F on BC, G on CD, and H on DA, then for any point P on the inscribed circle,