Square
Definition
A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ABCD.
Properties
The properties of a square include:
- All sides of a square are of equal length. This means that if one side is of length 'a', then all sides are of length 'a'.
- All angles of a square are right angles. This means that each angle of a square is 90 degrees.
- The diagonals of a square are equal and bisect each other at right angles. This means that if you draw a line from one corner of a square to another, it will cut the square into two equal parts, and the angle where the lines meet will be a right angle.
- The diagonals of a square bisect its angles. The line drawn from one corner of the square to another will cut the right angle into two equal parts, each measuring 45 degrees.
- The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.
Formulas
The formulas associated with a square include:
- Area of a square: A = a², where 'a' is the length of the side.
- Perimeter of a square: P = 4a, where 'a' is the length of the side.
- Diagonal of a square: d = a√2, where 'a' is the length of the side.
In Other Fields
In addition to its presence in geometry, squares have various applications in other fields as well.
In Algebra, the term "square" is used to refer to the operation of multiplying a number or expression by itself.
In Statistics, the square of the standard deviation is known as the variance, a key concept in the field of statistics and probability theory.
In Computer Science, squares are used in various algorithms and data structures, particularly those dealing with graphics and geometry.