GEOMETRY

     Geometry is one of the oldest branche of mathematics. It is concerned with properties of spaces such as the distance, shapes, size and relative position of figure. A mathematician who works in the field of geometry is called a geometer. 

    The most common type of geometry are plane geometry ( dealing with objects like the point,line, circle, triangle,and polygon ) , solid geometry ( dealing with objects like the line, sphere and polyhedron ) , spherical geometry ( dealing with objects like spherical triangl and spherical polygon ) . 

    Geometry is used in various daily life application such as art, architecture, engineering, robotics, astronomy, sculptures, space, nature, sports, machines, cars and much more. Geometry is the fourth math course in high school and will guide you through other things like points, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, circle, area and transformations. 

 MAJOR BRANCHES OF GEOMETRY

Euclidean geometry :

  Euclidean geometry is the study of geometrical shapes ( plane and solid) and figures based on different axioms and theorems. It is basically introduced for flat surface or plane surface. Euclidean geometry has practical application in computer science, crystallography, and various of modern mathematics. 

   RULES OF EUCLIDEAN GEOMETRY  

1) Things which are equals to the same things are equals to one another. 

2) If equals are added to equals, the wholes are equal. 

3) If equals are subtract from equals the remainder are equal. 

4) Things which coincide with one another are equal to one another. 

  Non euclidean geometry : 

    Non euclidean geometry is the study if geometry on surfaces which are not flat. Because the surface is curved, there are no straight line. 

    No  euclidean geometry is used to state the theory of relativity where the space is curved. The measurement of the distance, areas, angles of different parts of the earth is done with the help of no  euclidean geometry. Also non euclidean geometry is applied in celestial mechanics.  

    There are three types of non euclidean geometry -

1) Elliptic geometry

2) Hyperbolic geometry

3) Three dimensional non euclidean geometry. 

  Analytic geometry :

     Analytic geometry also known as coordinate geometry or Cartesian geometry, is the study of geometry using the coordinate system. Analytic geometry is used in physical and engineering and also in aviation, rocketry, space science and spaceflight. 

     Analytic geometry has four maine types  :

1) Descriptive

2) Diagnostic 

3) Predictive

4) Prescriptive . 

  The fundamental principle of analytic geometry is to describe the position figure such as points, lines, curves etc.., in coordinate system. 

  Projective geometry :

     Projective geometry is the branch of the mathematics that deals with the relationship between geometric figures on the images, or mapping, that results from projecting them onto another surface. 

    They are useful in the technique of artistic photography and industrial design as well as I  architecture. 

    Projective geometry are characterised by the " Elliptic parallel" axioms that any two planes always meet in just one line, or in the plane, any two lines always meet in one point. 

   Differential geometry : 

      Differential geometry is a mathematical discipline that study the geometry of smooth shapes and smooth curves otherwise known as smooth manifolds. It uses the technique of differential calculus, integrals calculus, linear algebra and multilinear algebra. 

     Differential geometry plays I  fundamental role in mathematical physics for instance, general relativity is the theory of spaces, time and gravity formulated by Einstein using the method of differential geometry. Differential geometry was founded by GASPARD MONGE and C. F. GAUSS in the beginning of 19th cent. 

    Topology :

     Topology is concerned with the properties of a geometric object that are preserved under continues deformations, such as stretching, twisting, crumpling and bending  that is without closing holes, opening holes, tearing gluing, or passing through itself. The fundamental concept of topology such as continuity compactness and connectedness, can be defined in terms of open sets. 

  There are two types of topology

1) Physical topology

2) Logical topology. 

   In computer networks a topology is used to explain how a network is physically connected and to logically flow of information in the network. A topology mainly describe how device are connected and interact with each other using communication link.