Section 3 GeoGebra
¶GeoGebra is a remarkable tool allowing simultaneous manipulation of both geometric and algebraic objects. Furthermore, it is written in HTML5, and therefore can be embedded easily in web pages. Finally, it is freely available, not only for use with a browser, with storage in the cloud, but also as a downloadable app for most operating systems.
For all of these reasons, this book uses GeoGebra throughout.
A simplified version of the default drawing interface is shown in Figure 3.0.1. You can select tools from the toolbar at the top of the drawing window, then use them to construct geometric objects in the Euclidean plane. You can pan the window by selecting the pointer tool (far left), then using the mouse to drag an empty part of the drawing window, and you can zoom using the scroll wheel on your mouse.
In this simplified interface, the undo/redo buttons do not work, nor can you save your work. To access those features, install the app or work directly on the GeoGebra website. You can, however, select and move (independent) objects, while preserving their relationship to other (dependent) objects. And you can reset the window to its original (empty) state by clicking on the circular arrows in the top right corner. (These arrows may not appear until you click the window in that corner.)
Most of the tool icons are self-explanatory, but in this simplified interface neither the tool names nor the help text indicating which objects should be selected are shown. When in doubt, experiment! If that doesn't suffice, try the web interface. When using that interface, each menu item displays the name of the tool, and selecting (or mousing over) a tool tells you what to do next. If that's still insufficient, complete documentation is available in the GeoGebra manual. 1
GeoGebra also has a drawing interface for graphics in three dimensions, a simplified version of which is shown in Figure 3.0.2. You can select tools from the toolbar at the top of the drawing window, then use them to construct geometric objects in Euclidean space. The scroll wheel will still zoom. Now, however, dragging an empty part of the drawing window with the mouse will rotate the viewpoint. (It can be helpful to select Zoom to Fit from the right-click menu before rotating the viewpoint, as this setting also centers the origin.) Furthermore, if you click and drag an image and then let go while your mouse is moving, the object will continue to rotate! In order to pan, hold the shift key while dragging.
The three-dimensional interface only allows points to be created on the grid shown. However, once created, points can be moved either horizontally or vertically, but not both at the same time. Toggle between these two modes by clicking on the point. (You can hide the grid by right-clicking on the background and deslecting it.)
Again, in this simplified interface, the undo/redo buttons do not work, nor can you save your work. To access those features, install the app or work directly on the GeoGebra website.