In math, we call graph for the drawings that drawn in paper or on screen to show variation of state of objects and events in one or more (at least one) dimension.
If a graph has more than two dimension, I prefer
to use graph space phrase to make it unite
with space concept. Although math. includes all kind of graphs, for
graph space that use for ploting mathematical curve equations, I
also use the name, the math. space.
The math. space is a imaginary environment that has defined rules and we use it to visualize our numeric thoughts. By using pen and paper or computer programs like 3DMath Explorer, actually we try to draw projection of this space on a 2 dimensional plane. (taking 2 dimensional pictures of 3 dimensional graphs)
Now let me give you some feature of the math. space.
• Some objects that defined in math. space can be exist in reel world and all objects in reel world can be defined in math. space.
• Because of math. space is an imaginary world, there is no universal gravity that exist between objects in reel world exist between objects that defined in this space.
• Objects defined and visualized in math. world have not density so they also have not solid, liquid and gas states. Maybe they have borders (but mostly they haven’t).
• However how much colorful we plot the graphs, in reality they haven’t got colors. (Color is not one of their properties. We use colors only to make graphs more understandable.)
• In reality the curves are only integrity of coordinates. To make this coordinates visual, we use methods like point, line and polygon.
• Curves have usually unlimited number of coordinates. So to plot them, we are using neighbor and limited number of coordinates of curves that have equal distances to each other as possible.
Basic components that exist in graph space are
plane and curve
in complexity order. The curve includes other three components. I main, a curve that you define can simply express a certain point in space and all lines and planes in space can be define with curves. And also all kind of objects could make exist in graph space.
Point and function equations (that could be simple or complex, what ever their rank are) are usually plots on a plane in 2 dimensional coordinate systems that defined with x and y axis’s. On this plane all points defined with (x,y) pair coordinates. Not being z values in these coordinate definitions must not mistake you that they have not got z values. In fact all coordinates have a z values. Because of their being on XY plane, z values of these curves are constant and equal to zero. So by writing coordinates with (x,y) pairs, we do not have to write coordinates as (x,y,0) with z values that equals to constant zero. It is only a short form of coordinate expressions. In fact in space coordinate systems there is a fourth dimension, the time. If we want to define a complete coordinate definition in space, we have to define it with the time dimension as (x,y,z,t).
At this point let’s give you same knowledge about coordinate system (or make you remember them).