This graphing utility uses the Mathematica kernel to produce its images. Therefore, any functions that are in Mathematica are legal here. If you haven't used Mathematica before, there are a few things to know:

  • Most functions start with a capital letter and place brackets around their arguements. So Sqrt[x] is the squareroot of x, and ArcSin[y] is the inverse sin of y.
  • Multiplication can be indicated by a space or an asterisk (*). This means that x*y=x y. However, xy would be undefined.
  • Constants also begin with capital letters, like Pi, E, or I.
  • The natural logarithm (base E) is Log[x], while Log[b,x] is the logarithm with base b of x. i.e. Log[x]=Log[E,x]
  • Brackets ([]) are reserved for functions and their options. To override Mathematica's order of operations, you must use parenthesese (()). The curly braces ({}) are reserved for lists.
  • In Mathematica, you do not have to type the ten in scientific notation. For example, 3.4*10^3=3.4*^3=3400.
  • If you would like to have a constant in your expression, use the letter a. For purposes of coloring, a is given a value of one, but it is shown as a symbol in all formula output. Be careful: while a*x can be represented as a x, it is different than ax, which is undefined.
  • If you make an error in typing in your graph, it will be reset so that {x,y,z}={0,0,0} for all values of x and y (or u and v). If you make an error typing in the range of variables of your graph, they will be changed to -1 or 1, or otherwise modified.

In the image coloring, red is positive, while blue is negative. Green is zero.

To show the images, this page uses a java applet available on the web. There are several ways to interact with the applet:

  • Drag with the left mouse button to rotate the image. Release the mouse button while dragging to spin the image.
  • While holding the shift key: drag up to shrink the image, down to enlarge, right to rotate the image clockwise, and left to rotate the image counter-clockwise.
  • Drag down with the right mouse button to remove sections of the image. This allows you to view inside solid objects if needed. To replace the sections, drag up.
  • Press the s key to split the image into two images that can be viewed stereoscopically. Stare through the image to see a three dimensional renderring. Press the s key again to reverse the images, so that you cross your eyes to see it. Press the s key one last time to return the image to normal.
  • While holding down the control key, drag the mouse to change the stereoscoped images.