1.2. Coordinate System and Plot Types with Their Dimensions
Coordinate system is a method
for defining positions of objects. We call the position of an object
as coordinate of the object and we call the system that
the object exists in as Coordinate system .
In coordinate systems we usually meet coordinate definitions as (x,y) or (x,y,z). In this systems, (x,y) pair coordinate defamations show that the coordinate is on a two dimensional plane (the XY plane) that z values constant zero. Hence coordinate definitions like (x,y,z) shows it is in a 3 dimensional space.
On the other hand there is other two coordinate definitions that we meet fairly less. The first of them is the definition with an axis name and a constant value (like x=5.3) that the coordinate has on this axis. With this definition we can both define coordinates on three main axis’s; x, y and z and on any other axis's named with any letters like k, l, m and with any directions in the space. This coordinate definition is taught as a start topic of coordinate systems in the books. But it does not considered as a sufficient coordinate definition. So people do not use it except the start topics.
The fourth type of coordinate definition is include the time variant as a fourth dimension with (x,y,z) coordinates that are in a 3 dimensional space. With time variants this type of coordinates are define as (x,y,z,t).
At this point a question may be came into your head. You may say that (x,y,z) defines a coordinate in 3 dimensional space and as this coordinate will never change with time then why should we need the 4th dimension in a coordinate system. However much this question seems to be a correctly asked question as content, in reality it only express one of our big mistakes. Yes, the graph space has three dimensions and any location in this space does not change with time. But on the other hand objects that exist in this space are changeable with time. As an 4th dimension the time shows condition and location changes of objects. I main, the time (t) also is a location axis like a, y an z and It is needed to put out exact location of objects.
Equivalence of coordinate system is
graph space or the mathematics spacein 3DMath Explorer. Graph space is
expressed with 3 axis’s (x, y and z axis’s) one for each dimension
at most. You cannot add a 4th axis to this system in projection. But
this does not mean that you cannot show 4th dimension. To show 4th
dimension, two methods can be use. First one of them to draw graphs
that change with time in the same time, just like to be occurred at
the same time segment. But they could be drown with different shapes
(for example with different colors, line width or shapes). The
second one is to separately draw changes of graphs in time with
cross-sections. We usualy call this second kind of graphs as
animated graphs .
The time is really one of most often used axes in coordinate definition systems. There are many graphs that change with time are drawn for most aims. But it mast be difficulty in plotting 3 dimensional location graphs that we do quite little meet 4 dimensional location graphs that add the time as a 4th dimension to this mass.
After all this information we can divide graphs into 4 groups for the coordinate systems that they plotted in. They are;
One Dimensional (1D) Graphs
• plotted in single dimensional coordinate systems
• They have only one axis
Two Dimensional (2D) Graphs
• They are plotted in two-dimensional coordinate systems
• They have two axes
Three Dimensional (3D) Graphs
• They are plotted in three-dimensional coordinate systems
• They have three axes
Four Dimensional (4D) Graphs
• They are plotted in four-dimensional coordinate systems
• They have three real axes and one imaginary axis
In addition to these graphs we
sould also mansion about graphs that have more than 4 dimension, they are n dimensional
graphs. Although these graphs would be more complicated to understand,
it is also possible to draw them in a 3 dimensional
coordinate system. These graphs like four dimensional graphs have three
real axes's and n - 3 imaginary axis's.
N Dimensional (ND) Graphs
• They could be plotted in four-dimensional coordinate systems
They have three real axes's and n - 3 imaginary axis's