Coordinates
are sets of numbers that describe position-- position along a
line, on a surface or in space. Latitude and longitude, or declination
and right ascension, each is a system of coordinates on the surface
of a sphere--on the globe of the Earth or the globe of the heavens.
Coordinates on a Flat Plane
René Descartes
A more widely used system are cartesian
coordinates, based on a set of axes perpendicular to each other.
They are named for Rene Descartes ("Day-cart"), a French
scientist and philosopher who back in the 1600s devised a systematic way
of labeling each point on a flat plane by a pair of numbers. You may
well be already familiar with it.
The system is based on two straight lines
("axes"), perpendicular to each other, each of them marked with the
distances from the point where they meet ("origin")--distances to the
right of the origin and above it, the origin being taken as positive and
on the other sides as negative (see drawing below).
The distance on one axis is named "x" and on the other axis "y". Given
then a point P, one draws from it lines parallel to the axes, and
the values of x and y at their intersections completely define the
point. In honor of Descartes, this way of labeling points is known as a
cartesian system and the two numbers (x,y) that define the
position of any point are its cartesian coordinates.
Graphs use this system, as do some maps.
This works well on a flat sheet of paper, but the real world is
3-dimensional and sometimes it is necessary to label points in
3-dimensional space. The cartesian (x,y) labeling can be extended to 3
dimensions by adding a third coordinate z. If (x,y) is a point on the
sheet, then the point (x,y,z) in space is reached by moving to (x,y) and
then rising a distance z above the paper (points below it have negative
z).
Very simple and clear, once a decision is made
on which side of the sheet z is positive. By common agreement the
positive branches of the (x,y, z) axes, in that order, follow the thumb
and the first two fingers of the right hand when extended in a
way that they make the largest angles with each other.
What follows uses the trigonometric functions
sine and cosine; if these are not familiar to you,
go learn about them her.
Previous
![[Image:(x,y)]](../../images/Sxy.gif)
The distance on one axis is named "x" and on the other axis "y". Given
then a point P, one draws from it lines parallel to the axes, and
the values of x and y at their intersections completely define the
point. In honor of Descartes, this way of labeling points is known as a
cartesian system and the two numbers (x,y) that define the
position of any point are its cartesian coordinates.
![[IMAGE:3-D Coord]](../../images/S3D.gif)
This works well on a flat sheet of paper, but the real world is
3-dimensional and sometimes it is necessary to label points in
3-dimensional space. The cartesian (x,y) labeling can be extended to 3
dimensions by adding a third coordinate z. If (x,y) is a point on the
sheet, then the point (x,y,z) in space is reached by moving to (x,y) and
then rising a distance z above the paper (points below it have negative
z).