Change of Coordinate Systems
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|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). |
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+ | Points can even be transferred to a different kind of coordinate system. A common example is mapping rectangular Cartesian Coordinates to Polar Coordinates. | ||
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|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 |
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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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