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Pisces Tutorial

Pisces is an application that is being developed at the Geometry Center in Minnesnowta. The purpose of Pisces is to create a platform for studing implicit equations. Implict equations are mathematical statements that are either true or false. An example of this would be the statement

. For some values of x and y the statement is true, for others it is not. What Pisces does is figure out what values of x and y make this statement true. Those values can then be graphed and we can see where in x and y space the values are grouped. In this case the graph is a circle.

The values In most implicit equations the graph is a curve and not just a bunch of scattered points.

Implict equations arise in several different mathematical situations. Most often they are used to find stable equlibria in differential equations. Differental equations are used to model real life things like deer populations and traffic flow. Equlibria occur when things are not changing. By finding these spots you can tell how hard it is for the system to stay around them.

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