There are a variety of tools available in Geometry Explorer for exploring geometric quantities relative to a coordinate system. The built-in coordinate system is constructed from two lines meeting at right angles at a point called the origin. Additionally, there is a point on the horizontal axes (x-axis) called the unit point. The distance from the origin to the unit point serves as the basic unit of measurement in the coordinate system.
All actions involving the coordinate sytem are controlled through the menus under the "Graph" menu.
(Show/Hide) Axes: Coordinate axes are always available in a Geometry Explorer Euclidean session. However, the axes are hidden initially. To see the axes use this menu option. Once the axes are visible, the menu item will change to "Hide Axes", allowing one to make the axes invisible. Tic marks are shown on the axes to help identify coordinate values. Slightly longer tic marks denote multiples of the unit length (2,3,4,etc.).
Grid (On/Off): This menu option will toggle on and off a grid for the coordinate system. To enable this option, the coordinate axes must first be visible. Note: Having the grid on will slow down the dynamic behavior of Explorer considerably. Use the grid only when absolutely needed.
Add Function to Graph: This menu option will bring up a dialog box for defining a function to graph in the Canvas. Look here for an example.
Add As (x,y) Point from Measures: We can add coordinate pairs to the axes by selecting (in order) 1) the measurement that will serve as the x-coordinate and 2) the measurement that will serve as the y-coordinate. Look here for an example.
Add Point on Function from x-Point: We can attach a point to the graph of a function defined from an existing point in the Canvas by selecting (in order) 1) the graph of the function and 2) the existing point and then choosing this option. Look here for an example.
Iterate Function from Point: If we select a point and the graph of a function f(x) we can iterate the function on this point as many times as we wish. Look here for an example.
Derivative of Function: Use this option to graph the derivative of a function. To enable this item select the graph of a function.
Input Box for Function: Use this option to create an input box for the graph of a function. The input box will appear in the Canvas and can be used to type in a new definition of the function being graphed. To enable this item select the graph of a function.
Function Resolution: Use this option to change the plotting resolution of the graph of a function. To enable this item select the graph of a function.