Difference between revisions of "Origin"

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The '''origin''' of a [[coordinate]] system is the [[center]] point or [[zero]] point where the [[axe]]s meet.
  
The '''origin''' of a [[coordinate]] system is the [[center]] point or [[zero]] point where the axes meet.
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==In Euclidean Systems==
 
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In the Euclidean [[plane]] <math>\mathbb{R}^2</math>, the origin is <math>(0,0)</math>. Similarly, in the Euclidean [[space]] <math>\mathbb{R}^3</math>, the origin is <math>(0,0,0)</math>. This way, in general, the origin of an <math>n</math>-dimensional Euclidean space <math>\mathbb{R}^n</math> is the <math>n</math>-tuple <math>(0,0,\ldots,0)</math> with all its <math>n</math> components equal to zero.
In the Euclidean plane <math>\mathbb{R}^2</math>, the origin is <math>(0,0)</math>. Similarly, in the [[Euclidean space]] <math>\mathbb{R}^3</math>, the origin is <math>(0,0,0)</math>. This way, in general, the origin of an <math>n</math>-dimensional Euclidean space <math>\mathbb{R}^n</math> is the <math>n</math>-tuple <math>(0,0,\dots,0)</math> with all its <math>n</math> components equal to zero.
 
  
 
Thus, the origin of any coordinate system is the point where all of its components are equal to zero.
 
Thus, the origin of any coordinate system is the point where all of its components are equal to zero.
  
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[[Category:Definition]]
 
[[Category:Definition]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Latest revision as of 19:12, 15 November 2007

The origin of a coordinate system is the center point or zero point where the axes meet.

In Euclidean Systems

In the Euclidean plane $\mathbb{R}^2$, the origin is $(0,0)$. Similarly, in the Euclidean space $\mathbb{R}^3$, the origin is $(0,0,0)$. This way, in general, the origin of an $n$-dimensional Euclidean space $\mathbb{R}^n$ is the $n$-tuple $(0,0,\ldots,0)$ with all its $n$ components equal to zero.

Thus, the origin of any coordinate system is the point where all of its components are equal to zero.

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