by Sithambaranathan Prithiviraj

Created on: May 06, 2008

A square is a quadrilateral where all four sides are equal and the 4 angles are 90 degrees. In essence square is a special quadrilateral. Six sides made up of square shape can produce a cube.The square also produces 4 identical or congruent right angle traingles irrespective of of the length of the four sides of the square.In other words understanding squares is vital to understand other quadrilaterals and also square is related to other figures and the concept of area.

In nature some crystals are cubes. In geometry square or 1unit squares are used to measure areas. For example the area is measured in length squares irrespective any 2 dimensional shapes.In addition square is used as windows and also used as square bricks because of its unique geometric properties in building construction.

In a grid paper, squares are used and it represents the X-Y co-ordinates and it enables to draw graphs as well by counting the number of squares and multiplying by the area of one square one can get the area under the curve and the x axis and Y axis.

In geometry there is a relationship between the three sides of a right angle triangle in its square form. That is, the square drawn in either sides of a right angle triangle is equal to the triangle drawn on the hypotenuse. This is called Pythagoras theorem. In addition, the proportion of the sides and the diagonal irrespective of the length of the sides is always one is to square root of two. That is the ratio is a constant for all squares. AS well, the diagonal splits are square area equally and they are congruent triangles.The squares and right-angled triangles in different combinations can produce beautiful tessellations. These tessellations can be useful to draw geometrical art and it gives eye catching shapes.

If one draws a outside circle of a square, the remaining area and the area of the square is always a constant irrespective of the length of the side of a square. The difference of a diamond shape and a square is that in a diamond the angle between the four sides is not 90 degrees compared to a square. That is if a square is tilted then it becomes a diamond. In other words a transformation of a square can give the shape of a diamond. As discussed above square is an important geometric figure in mathematical sense as well it has some practical uses in art, graphical constructions and tessellation formations. In summary the concept of square has some unique properties in a geometrical sense and its mathematics is facinating as well as practical usefulness in real life.

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