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# Regions and their Signed Areas

## Highlighting Regions in GC

As explained in Chapter 3, GC is built to create graphs. It is designed to interpret anything you type as either a definition of a mathematical term (e.g., a function) or a command to create a graph. Essentially, any well-formed statement that you type, other than a definition, will cause GC to generate a graph.

We describe regions in the plane by stating conditions that points in the plane must satisfy to be considered in that region. For example, the mathematical statement $\left\{(x,y)\mid x^2+y^2\le 1\right\}$, read as "The set of all points with coordinates x and y such that ...", describes the set of points in Figure 8.3.0-1 (apologies for the weird numbering). GC highlighted all the points in the Cartesian plane that have coordinates x and y such that $x^2+y^2\le 1$.

Figure 8.3.0-1. Typing $x^2+y^2\le 1$ into GC told it to highlight all the points in the plane whose coordinates satisfy that condition.

Notice that in Figure 8.3.0-1 we typed only the condition part of the mathematical statement. This is because GC always interprets any non-definitional statement involving x or y as a command to "highlight all the points (x,y) such that ...".