Mathematics Coordinate Geometry Coordinate System - Cartesian and Polar Coordinates

Coordinate System – Cartesian and Polar Coordinates

-

Coordinate System – Definition


Coordinate system in Geometry is a system of one or more numbers, which uniquely determine the position (left-right, top-bottom, up-down) of the points or other geometric elements on a manifold such as Euclidean Space. -which is two dimensional, three dimensional or n-dimensional space. There are numbers of coordinate system commonly used in geometry. Number line, Cartesian, Polar, Cylindrical etc. In this article we will discuss about Cartesian and Polar Coordinate System and their relationship.[mathjax]

Cartesian Coordinate System


Cartesian Coordinates are rectilinear two-or-three-dimensional coordinates. For two dimension, it specifies each point uniquely in a plane by a pair of numerical coordinates, $(x,y)$. Cartesian coordinate is also familiar as rectangular coordinates, because it is like moving in a box. René Descartes (1596-1650), a French philosopher, mathematician, and scientist. He shows a very strong connection between Geometry and Algebra.

let an algebra: $y = 2x-1\quad\text{…eqn(1)}$. Here for every arbitrary $x$ value, we find an associates $y$ fron the equation.

$x$ $y$
$x=-2$ $y=2.(-2)-1=-5$
$x=-1$ $y=2.(-1)-1=-3$
$x=0$ $y=-1$
$x=1$ $y=2.1-1=1$
$x=2$ $y=2.2-1=3$

$x$ is an independent variable and $y$ here a dependent variable. Because we can choose the value of $x$ independently. and value of $y$ depends upon $x$. Graph below visualize the relationship between $x$ and $y$ for the Algebra in $eqn(1)$. Two perpendicular $X$ and $Y$ axes intersect each other on a point $(0, 0)$, therefore, the point is the origin of two axes.

coordinate system
For every possible $x$, the pair of numerical coordinates, $(x, y)$ creates a straight line on the plane. The line is clearly a relationship between Geometry and Algebra, because every point on the straight line is a solution for $eqn(1)$. René Descartes first shows this relationship, between Algebra and Geometry. Therefore the coordinates that specify these points on the straight line is called Cartesian Coordinates, and the equation is called linear equation.

Polar Coordinate System


Polar Coordinate is a two dimensional coordinate system, in which each point on the plane is specified by a radical distance $r$ from the reference point $0$, and an angular rotation $θ$ from the reference axis $X$. Direction of $X$ is called reference direction.

The reference point $0$, analogous to the origin of a Cartesian coordinate system, which is the pole. The straight line from the pole in the reference direction is the polar axis. distance from the pole is radius $(r)$, angle from reference direction is polar angle $(θ)$.

polar coordinate system

Next we will see the relationship between these two Coordinate Systems and their conversion.

LEAVE A REPLY

Please enter your comment!
Please enter your name here

Latest Articles

Dictionaries | HashMap in Python | Working with Key-Values

Dictionaries in Python is similar to Hashmap comparing to other languages. It stores data as a key-value...

Hash Table | Indexing | Hashing Algorithm | Python Implementation

This article will talk about a high-level view of the Hash Table. As a programmer, this technique...

Eigenvector Eigenvalue | Linear Algebra Fundamentals

Eigenvector ($bar{v}$) in linear algebra is a non-zero vector (matrix) that doesn't change its direction during linear...

Pivot Table | Microsoft Excel | Create Data Insight Easily

Pivot table in microsoft Excel is an useful function that gives us a way to create insight...

Macro Function in Microsoft Excel | Automate Repetitive Task

This article we will talk about the Macro. It is a function in microsoft excel which basically...

SVD | Singular Value Decomposition | Machine Learning Fundamentals

Singular Value Decomposition or SVD is the general purpose useful tool in Numerical Linear Algebra for data...

Must read

Dictionaries | HashMap in Python | Working with Key-Values

Dictionaries in Python is similar to Hashmap...

Eigenvector Eigenvalue | Linear Algebra Fundamentals

Eigenvector ($bar{v}$) in linear algebra is a...

You might also likeRELATED
Recommended to you