



When we
had the equation:



X^{2}
+ Y^{2} = 25






We set up
a graph with an X and Y axis 


to draw
the equation line on, like this: 











The graph
line turned out to be a circle with a radius of 5, 


that is,
every point was 5 units from the center of the circle. 











Now what
if we had an equation like: 





X^{2}
+ Y^{2} + Z^{2} = 25






Every
point is still 5 units from the center, 


but now
we have 3 variables. 


To graph
this, 


we would
need to set up a graph with three axis. 


Like
this: 











Now the
X, Y, Z graph looks kind of funny. 


What it
is supposed to be is: 


The X
axis goes left and right. 


The Z
axis goes up and down. 


AND 


The Y
axis goes into and out of the page. 





It's a 3
dimensional object, 


and you
can't build a 3 dimensional object correctly 


on a 2
dimensional graph. 





It's kind
of like drawing a cube. 











You have
to use your imagination a bit. 





So what
does a 3 dimensional object, 


where all
of the points are 5 units from the center, 


look
like? 











A BALL! 





We could
add and subtract values from any of the variables 


to move
the ball around. 


This
works just like it did 


when we
graphed other things in the last few pages. 





In math,
we can use as many variables in an equation as we want. 





But once
we get past 2 or 3, 


graphing
gets pretty tough. 


AND 


We
usually need special techniques to solve them, 


mostly
using computers. 





copyright 2005 Bruce Kirkpatrick 
