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Geometry is the branch of mathematics that deals with the study of shapes and their properties. Geometry is often considered to be the fun aspect of the field of mathematics. Geometry is an ancient subject that dates back to as early as the time of the 2nd millennium B.C. The subject mainly focuses on 3 elements namely:
1. Length – Length is the size of a line segment.
2. Area – Area is the size of a closed region in a plane.
3. Volume – Volume is the size of a solid.
Earlier in Geometry, the various proofs were constructed by the use of only the compass and the straight edge. But contemporary Geometry involves the use of instruments like the compass, ruler, divider, protractor, Set Square, T-square, ellipsograph and the opisometer.
In the current time, Geometry can be sub divided into the following:
• Euclidean geometry
• Differential geometry
• Algebraic geometry
• Topology
Let’s discuss them in detail:

• EUCLIDEAN GEOMETRY – The classical sense of geometry is Euclidean Geometry. Euclidean geometry includes the study of angles, triangles, circles, solid figures, similarity and congruence. Euclidean geometry is also applicable in crystallography, computer science and different branches of modern mathematics.
• DIFFERENTIAL GEOMETRY – Differential geometry uses techniques of linear algebra and calculus to study the problems of geometry. It is applicable in physics (includes general relativity).
• ALGEBRAIC GEOMETRY – Algebraic geometry studies geometry through the use of polynomials and other algebraic techniques. It is applicable in various areas of string theory and cryptography.
• TOPOLOGY – Topology deals with the properties of geometry that are unaffected by the continuous function. Topology basically deals with large scale properties of a space, such as compactness and connectedness.

Some of the important concepts of geometry are:

• AXIOMS – Axioms are the statements about real numbers, they are also called algebraic postulates. When it comes to measuring figures, real numbers are an important part of geometry and hence axioms are very useful.
• POINTS – Points are the fundamental objects of Euclidean geometry. A point in geometry is a location, it has no length, no width and no depth or in short we can say that it has no size. A line is a combination of points that extends infinitely in two directions.
• LINES – As discussed in the last point, a line is a combination of points along a straight path that goes on and on in opposite direction and a part of line that have two end points is called as line segment.
• PLANES – A plane is a flat, two dimensional surface that extends infinitely far.
• ANGLES – An angle can be defined as the inclination to each other in a plane (two lines which do not lie straight with respect to each other). An angle of 90 degrees is called a right angle and an angle of 180 degrees is called a straight angle. And an angle that is larger than 90 degrees and smaller than 180 degrees is called an obtuse angle.
• CURVES – A curve is an object similar to a line but that is not straight like a line. A curve is a generalization of line.
• SURFACE – Surface is a two dimensional object. For example, sphere. A surface is described by a polynomial equation in algebraic geometry.
• TOPOLOGY – A topology is a mathematical structure that relates the elements spatially to each other.
• DIMENSION – Dimension is defined as the minimum number of coordinates needed to specify any point within it.
• SYMMETRY – The concept of symmetry is as old as geometry itself.

Geometry has applications in various fields. Some of them are discussed here:

• ARCHITECTURE – Architecture is related to mathematics because mathematics is used in architecture for several reasons. Architecture uses geometry for designing buildings.
• ARTS – Arts and mathematics are related to each other in a number of ways. Artists use geometrical elements to create a theme throughout their art work. And Artists use these geometrical elements (lines, shapes and angles) to create the illusion of the third dimension and it is known as optical art.
• PHYSICS – Physics is related to geometry when it comes to astronomy. Geometry is used in mapping the position of planets and stars on the celestial sphere and the relationship between movements of celestial bodies. According to the latest physics theory, string theory is also geometrical in nature.

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