Difference between revisions of "Origin"

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The '''origin''' is defined as the point where the x-axis, y-axis, z-axis, etc. meet. The origin is written as <math>(0)</math>, <math>(0,0)</math>, <math>(0,0,0)</math>, etc.
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The '''origin''' of a [[coordinate]] system is the [[center]] point or [[zero]] point where the [[axe]]s 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.
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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]]
 
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[[Category:Geometry]]
 
[[Category:Geometry]]
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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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