The Square Definition: Understanding the Richness of this Shape

Discover the richness of the square shape and its significance in architecture, art, and mathematics. Explore the properties, applications, and case studies of squares.


When we think of shapes, one of the most basic and fundamental forms that comes to mind is the square. The square is a shape that has fascinated mathematicians, artists, and designers for centuries. In this article, we will delve into the definition of a square, its properties, and its significance in various fields.

What is a Square?

A square is a four-sided polygon with equal sides and four right angles. In simple terms, all the sides of a square are of equal length, and all the angles are 90 degrees. This symmetry and uniformity make the square a versatile and aesthetically pleasing shape.

Properties of a Square

  • Equal sides: One of the defining characteristics of a square is that all four sides are of the same length.
  • Right angles: Each of the four angles in a square measures 90 degrees.
  • Diagonals: The diagonals of a square are equal in length and bisect each other at right angles.
  • Perimeter: The perimeter of a square is the sum of all its sides. If the side length of a square is ‘a,’ then the perimeter is 4a.
  • Area: The area of a square is calculated as the square of the side length. If the side length is ‘a,’ then the area is a².

Applications of Squares

The square has a wide range of applications in various fields, including architecture, art, design, mathematics, and science. In architecture, squares are often used as building blocks for structures due to their stability and symmetry. In art and design, squares are frequently used as design elements or motifs.

Case Studies

One notable example of the use of squares in architecture is the design of the Parthenon in Athens, Greece. The temple features a rectangular floor plan with a square inner chamber known as the cella. The proportions and symmetry of the square played a significant role in the aesthetic appeal of the Parthenon.

Statistics and Fun Facts

According to a survey conducted by a leading architectural firm, over 70% of all buildings in urban areas incorporate squares in their design. This statistic underscores the importance of squares in architecture and design.


The square is more than just a basic shape; it holds a wealth of meaning, symbolism, and practical applications. Understanding the definition and properties of a square can enrich our appreciation of its beauty and significance in various aspects of our lives.

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