Change of Coordinate Systems

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Change of Coordinates

The same object, here a circle, can look completely different depending on which coordinate system is used.


Basic Description

It is a common practice in mathematics to use different coordinate systems to solve different problems. In two dimensional space, suppose we take a set of points in regular x-y Cartesian Coordinates, represented by ordered pairs such as (1,2), then multiply their x-components by two, meaning (1,2) in the old coordinates is matched with (2,2) in the new coordinates. A set of points would become stretched in the horizontal x direction since each point becomes further from the vertical y-axis (except for points originally on the y-axis, which remain on the axis).

Points can even be transferred to a different kind of coordinate system. A common example is mapping rectangular Cartesian Coordinates to Polar Coordinates.

A More Mathematical Explanation

Points in one space are undergo a transformation of some kind to be mapped to a points in another spa [...]

Points in one space are undergo a transformation of some kind to be mapped to a points in another space.




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