Part 11: Graphing Equations in Three Dimensions (Optional)

1. Now we are going to try some three-dimensional plotting.  Make sure x, y, and z are unassigned.  Type the equation
   x^2 + y^2 + z^2 = 25
   Use your mouse to highlight this expression, click the right mouse button, and select "Plots"  > "Plot Builder" from the popup menus.  If there are two text boxes, make sure the first text box says "Plot" and the second box says "3-D implicit plot".  If there is only one text box, click where it says "3-D implicit plot".  ("Implicit" means we are graphing an equation, not necessarily a function.)  Down below that it might say "Parameter 1", "Parameter 2", and "Parameter 3".  It should also say "x" and then two boxes with numbers in them.  Similarly, there should be with "y" and "z".  You may leave the numbers or change them if you want.  If you do not see a plot, click the "Plot" button.  Maple should make an arrow pointing from your equation to its plot.  (Note that Maple may switch to Text mode without warning after the plot.)
   
   
2. When the plot appears, use your mouse to "select" it -- you should see a box around the graphic. Experiment with the rotation arrow, and the drag buttons at the corners and sides of the box. Experiment with the icons at the top of the screen to see what they do. In particular, obtain each of the following:
   
   
• A plot with normal axes
  
  
• A plot with boxed axes
  
  
• A plot with a wire frame instead of a solid surface
  
  
• Plots with and without the appropriate aspect ratio, i.e., the horizontal units are the same as the vertical units.
  
  
• A "zoomed-in" version of the plot.
  
  
• A "zoomed-out" version of the plot.
  
  
• A view of just the left-hand part of the plot.
  
  
• A view of just the bottom part of the plot.
  

3. You can also use the "Plot" menu at the very top of the Maple window to change the plot.  Experiment with the popup menus to see what they do.  In particular, obtain each of the following:
   
   
   • A plot with a green surface.
     
     
   • A plot where the surface is black at the bottom and white at the top.
     
     
4. Now type the equation
   x^2 + z^2 = 4
   Use your mouse to highlight this expression, click the right mouse button, and select "Plots"  > "Plot Builder" from the popup menus.   Notice that the second box says "2-D implicit plot", which is not what we want.  This is because the equation did not include a y variable.  Instead, highlight the expression, click the right mouse button, and select "Plots" > "3-D implicit plot" > "x, ?, z".   Did you get the picture you expected?  (This method bypasses several of the options in the Plot Builder, so you should be familiar with both menu selections.) 
   
   
5. You may feel that the pictures you are getting are too "jagged".  You can fix this when you are in the "Plot Builder" screen.  Type the equation
   x^2 + y^2 + z^2 = 25
   again, and select "Plots"  > "Plot Builder" from the popup menus.   This time click the "Options" button or the "3-D Options" text.  There are lots of boxes and menus here; in the lower right you should find "Grid Size".  Change it to a higher number or numbers and click "Plot".  What happened?  Feel free to play with the other boxes and menus on the "Options" page.