- published: 27 Jun 2010
- views: 45502
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.
The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point.
Why I thought I had it all
and why I wanted more
Could it be just there for while,
the while I need for myself
Never dared to seal my door
Never dared to look behind
Once again I was
As fool as I can be
Anger takes my mind at will
The will I never could lead
Feel this anxious rise
Got no chance to be myself
Maybe somewhere I´ll find
the place where I can just be
Let me allow this dawn
Before we´ll follow that star
I´m making my command
on this hazy unknown ground
(The) Pain and the anger is gone
I know my life is worth of this run
I won´t again put myself to burn my
Candle at both ends
Once we will break our time
And that shine in your eyes will be my guide
Looking into the stars
made me blindly believe
in the truth of the lighting star
It may be hard to tell in advance