# Change of Coordinate Systems

(Difference between revisions)
 Revision as of 11:17, 11 June 2009 (edit) (New page: {{Image Description |ImageName=Change of Coordinates |Image=Coordchange.JPG |ImageIntro=The same object, here a circle, can look completely different depending on which coordinate system i...)← Previous diff Revision as of 11:33, 11 June 2009 (edit) (undo)Next diff → Line 3: Line 3: |Image=Coordchange.JPG |Image=Coordchange.JPG |ImageIntro=The same object, here a circle, can look completely different depending on which coordinate system is used. |ImageIntro=The same object, here a circle, can look completely different depending on which coordinate system is used. - |ImageDescElem=It is a common practice in mathematics to use different coordinate systems to solve different problems. + |ImageDescElem=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. + |ImageDesc=Points in one space are undergo a transformation of some kind to be mapped to a points in another space. |ImageDesc=Points in one space are undergo a transformation of some kind to be mapped to a points in another space. |AuthorName=Brendan John |AuthorName=Brendan John

## Revision as of 11:33, 11 June 2009

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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