In mathematics, Euclidean space is a conventional 2D or 3D space where it contains a collection of geometrical points that produces a plane figure. Sometimes it is called as flat space. Most of the laws of geometry are valid only in the Euclidean space. Because the line produced by connecting two points in Euclidean space is always a straight line. It is also generalised to higher dimensions like four-dimensional space which is explained in Euclidean geometry. The space used for defining the points traditionally uses the standard geometry which is different from modern geometry.
In Euclidean space, it can be given with coordinates. If the space is 2-dimension in nature, each point has two coordinates (x andy) and if it is 3 – dimensional in nature, each point has three coordinates (x, y, and z ), where all the coordinates should be a real number and x, y and z are the distances from the respective axis like X, Y and Z which is clearly explained in coordinate geometry. When you connect the two points in the flat space, it will produce a line and again connect another point from the line. When this process goes on, a plane figure is formed in the Euclidean space. The most important law of geometry that uses Euclidean space is the Pythagorean theorem where it finds the distance between two points in the flat space. Nowadays, Euclidean space is commonly called a cartesian plane or cartesian space. It always involves various axioms and rules that define the position of an element. The postulates and axioms defined in Euclid’s space are also applicable in the real world. Some of the real-life applications that use Euclid’s space are as follows
- Describing the position of an object.
- In economics, it is used for analysing and managing the data.
- Used to describe the geographic locations using latitude and longitude position
- Used in air transport to find the location of aircraft in the sky.
- In military service, it is used to find the position of each soldier or an opponent.
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