Geometry and Trigonometry

The branch of mathematics that deals with the dimension, angles, shapes and sizes of the variety of the things that we see in our everyday life is known as ‘Geometry’. The meaning of the Greek word ‘Geometry’ stands for ‘Geo’ and ‘Metry’ which means ‘Earth’ and ‘Measurement’ respectively. In this branch of mathematics, we deal with the learning of various types of transformations, similarities and angles in the figures. Plane, point, line and angle are the basics on which this branch of mathematics is dependent. All the shapes in the branch of geometry are based on the aforesaid concepts.

Various branches of Geometry

Algebraic Geometry: The branch that deals with the study of the zero of the multivariate polynomials is known as a polynomial. Cryptography, string theory and so on are the applications of this branch. It includes the equations of linear and polynomial algebra that are beneficial in solving the sets of zeros.

Discrete Geometry: This branch of geometry deals with simple geometrical objects such as triangles, lines, points, and so on.

Differential Geometry: This branch uses the techniques of algebra and calculus for the sake of problem-solving. General relativity in physics and many more are the various problems that can be solved with this branch of geometry.

Euclidean Geometry: The branch of geometry that deals with the study of theorems and axioms including lines, angles, planes and solid figures. The branch is useful in a variety of branches such as in the modern-day problem solving of mathematics, computer science, crystallography and many more.

Convex Geography: it is the branch that uses the technique of real analysis in the Euclidean space of convex shapes. The branch holds applications in functional and optimization analysis in number theory.

Topology:

It is the branch of geometry that is concerned with the properties of space under continuous mapping. Consideration of continuity, filters, spaces, grills, clusters, branches and so on are the various applications involved in this branch of geometry.

Types of Geometry:

Plane Geometry: The flat shapes that can be put down on a piece of paper is known as plane geometry. The circles, lines and triangles of two dimensions are the inclusions for this. Another name for plane geometry is two-dimensional geometry. Length and breadth are the only two-dimensional figures in this type of geometry.

Point: The precise location on a plane is known as point. It is important to consider that a point is a place, not a thing. Also, the point has only position but not dimension.

Line: The has no curves and thickness and extends indefinitely without any end to it. The combination of indefinite points forms a straight line. In geometry, there are two types of lines, horizontal and vertical with x and y-axis respectively.

Angles in Geometry:

There are four types of angles in the branch of geometry. Those are acute angle, obtuse angle, right angle and the final one being the straight angle.

Acute angle: The angle that ranges between degrees from zero to ninety is known as an acute angle. The acute is always less than the right angle.

Obtuse angle: The angle that ranges between the degrees from ninety to one hundred and eighty degrees is known as an acute angle. The acute is always more than the right angle.

Right angle: The angle that is exactly equal to ninety degrees is known as the right angle. The right angle is always more than the acute angle and less than the obtuse angle.

Straight angle: The angle that is exactly equal to one hundred and eighty degrees is known as the straight angle.

Trigonometry:

The branch of trigonometry that deals with the study of triangles are known as trigonometry. More specifically the angle involved in the study of trigonometry is the right angle which is ninety degrees. Trigonometry helps us to find the missing sides or the angles of the triangle.

Functions of trigonometry:

Sine, Cosine and Tangent are the three basic functions of trigonometry that are popularly known by the abbreviations sin, cos and tan. Remembering the formulas of trigonometry will be difficult in the initial stages but can be learnt with practice over the period. The use of Trigonometry is related to finding the angles of the triangles and as the triangles are the simplest forms found in nature the branch of trigonometry becomes essential in deriving the conclusions for the problems arriving in day-to-day life. Apart from mathematics, be it in cartography, satellite systems, structural engineering, in the branch of architecture and so on the role of trigonometry plays a major role.

Relationship between Geometry and Trigonometry.

Trigonometry and Geometry are the two interlinked streams of Mathematics. On one hand where geometry deals with the study of triangles and circles, their shapes, degrees and other mathematical factors the stream of trigonometry deals with a variety of equations and approaches required to study the properties of circles and triangles (specifically the study of right angled triangles).

Conclusion:

Both geometry and trigonometry play a major role in everyday lives in various branches of science and mathematics as well. The branches of mathematics, geometry and trigonometry are interlinked to each other as both play a major role in finding the role of measurements of the triangles.  Formulas play a major role in both, geometry and trigonometry and using the appropriate formulas is the demand of both the inter-linked stream of mathematics (geometry and trigonometry).