Square
In geometry, a Square is a regular quadrilateral, which means it has four equal sides and four equal angles. Each of its angles measures 90 degrees, making it a special type of Rectangle where all sides are equal in length. Here are some key facts about squares:
- Properties:
- All sides are of equal length.
- All angles are right angles (90 degrees).
- Diagonals bisect each other at right angles.
- Diagonals are equal in length.
- It has rotational symmetry of 90 degrees.
- Formulae:
- Area = side²
- Perimeter = 4 × side
- Diagonal = side × √2
- History:
The concept of the square can be traced back to ancient civilizations. The Egyptians used the square in their architecture, particularly in pyramid construction, where the base of a pyramid is often a perfect square. The Greeks, known for their contributions to geometry, formalized many properties of the square through the works of mathematicians like Euclid in his "Elements," where he discusses squares in the context of other geometric shapes.
- Context:
- In mathematics, squares are used in algebra to express the squaring of numbers, in geometry for calculating areas, and in various other applications like graph theory and computer graphics.
- In architecture and design, squares are fundamental in creating balanced and symmetrical structures.
- In everyday life, squares appear in tile patterns, grids, and many urban layouts where city blocks are often designed in square shapes.
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