Geometry can be defined as the branch of math which deals with the relations and properties of point, line and solids. In Greek, the word geometry – ‘Geo’ stands for earth and ‘metry’ stands for measurement. Euclid is known as the ‘Father of Geometry’. The geometry was developed for measuring areas and calculating distance.
Main Categories and Divisions of Geometry
The 2 main categories of geometry are,
1. Plane Geometry: Plane geometry deals with 2-dimensional shapes which includes lines, triangles and circles. In 2-dimensional pictures we’ll be able to see only x-axis and y-axis but not the z-axis. Below you may see some of the examples of 2-dimensional shapes.
2. Solid Geometry or 3-Dimensional Shapes: Solid geometry deals with 3-dimensional shapes which includes cone, sphere and cube. In 3-dimensional pictures we’ll be able to see all 3 sides on an objects namely, x-axis, y-axis and z-axis. Below you may see some of the examples of 3-dimensional shapes.
Types of Geometry
- Euclidean Geometry: The Euclidean geometry helps us study about Euclidean geometry like flat surfaces etc. With the help of Euclidean geometry we can learn finding the circumference of a circle, area of circle etc. With it we get the popular ‘Pythagoras theorem’.
- Riemannian Geometry: The Riemannian geometry primarily helps us to study the curved surface like sphere, which is not a flat surface but a curved surface.
- Gravitational Lensing: Our universe can be identified as a 3 dimensional space. Just about the earth the cosmos appears roughly like 3 dimensional Euclidian space. Still, near very big black holes and stars the space is curved and flexed. The Hubble scope has detected points in space that hold more than one minimum geodesic to the telescope. These are known as gravitational lensing. The measure that space is curved could be approximated by applying theorems from Riemannian geometry and measures taken by astronomer. Physicists think that the curve of space is associated to the gravitational area of a star, as per partial derivative equation known as Albert Einstein Equation. So using the outcomes from the theorems in Riemannian geometry they could approximate the mass of the stars or black holes which drives the Gravitational lensing.
Normally, any math construction that has notion of curve would fall under the geometry. Some of these would include,
- Differential Geometry: This is the natural extension of linear algebra and calculus and it is simply called as “Vector Calculus”.
- Symplectic Geometry: Symplectic geometry helps in evolution of simple mechanical operations as well as theoretical aspects of physics.
- Semi Riemannian Geometry: This is a 4-dimensional geometry where Albert Einstein applied in the discoveries our cosmos.
- Algebraic Geometry: Algebraic geometry is used in polynomial equations and many difficult problems in number sense.