On the TI-Nspire, you can use a mixed view with an analytic window open on a Geometry page to explore the formula for the area of a circle. You also can use the Automatic Data Capture feature to generate a scatter plot of the area-versus-radius data. This approach is a bit complicated. However, this option has the benefit of adding numeric data to a Lists & Spreadsheet page.
If you attempt this construction, the circle is a bit tricky. First draw a horizontal line. Overlay a segment on top of the line and hide the line. Draw your circle so that the segment is the radius of the circle.
Here’s a brief description of how to accomplish this task.
Click each measurement once and press [VAR]→Store Var. Type a descriptive name for each variable (such as radius and area).
Notice that variable names appear in bold font. See the first and second screens.
Configure a Lists & Spreadsheet page for Automatic Data Capture.
Configure the entry line to draw a scatter plot of the area-versus-radius data.
Drag the point on the edge of the circle, and watch the scatter plot appear in the analytic window.
The scatter plot in this exploration is tied to the analytic window, which means if you adjust the window settings, the scatter plot adjusts accordingly.
It would appear that the scatter plot is quadratic — but what is the equation that models this data? Configure the entry line for function graphing and graph the function y = x2.
As shown in the first screen, move the cursor to the graph until the
appears and press [CTRL][CLICK] to grab the edge of the graph. As you see in the second screen, use the Touchpad keys to manipulate the graph to pass through the scatter plot and watch the equation update accordingly. It seems clear that the equation
is the formula that relates the area of a circle to its radius.