Square cake design

This article is about the polygon. All four sides of square cake design square are equal.

Opposite sides of a square are parallel. 2 case of the families of n-hypercubes and n-orthoplexes. The area of a square is the product of the length of its sides. Since four squared equals sixteen, a four by four square has an area equal to its perimeter. The only other quadrilateral with such a property is that of a three by six rectangle.

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. Because it is a regular polygon, a square is the quadrilateral of least perimeter enclosing a given area. Dually, a square is the quadrilateral containing the largest area within a given perimeter. This value, known as the square root of 2 or 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. A square has a larger area than any other quadrilateral with the same perimeter.

The square is in two families of polytopes in two dimensions: hypercube and the cross-polytope. The square is a highly symmetric object. Its symmetry group is the dihedral group D4. A square can be inscribed inside any regular polygon. The only other polygon with this property is the equilateral triangle. This equation means “x2 or y2, whichever is larger, equals 1.

The square is therefore the shape of a topological ball according to the L1 distance metric. The following animations show how to construct a square using a compass and straightedge. Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the square is r8 and no symmetry is labeled a1. The square has Dih4 symmetry, order 8. There are 2 dihedral subgroups: Dih2, Dih1, and 3 cyclic subgroups: Z4, Z2, and Z1. These 6 symmetries express 8 distinct symmetries on a square.