This is the first part of the GeoGebra 4.0 Sneak Peek Series. In this series, we are going to discuss some of the changes in GeoGebra from version 3.2 to 4.0. If you want to have a complete view of the changes, you can read the GeoGebra 4.0 Release Notes.

If you don’t know yet, GeoGebra 4.0 will be released by the end of August 2011. If you’re as excited as me and want to try out the new features, you might want to explore the GeoGebra 4.0 Beta release.  This release is, of course, not stable (they may still change some features), so if a dialog box appears asking you if you want to associate your GeoGebra file with it, don’t.

 

The most evident changes in GeoGebra 4.0 are the new tools. The tools, their icon, and their descriptions are shown below.  Some tools have no icons yet, so I left it blank. 

Icon	Name	Description
	Attach/Detach Point	Attaches/detaches a point to a particular object.
	Function Inspector	Displays different properties of functions (maximum, minimum, roots, etc). We will discuss this in a separate post.
	Insert Button	Inserts a command button in the GeoGebra drawing pad.
	Insert Text field	Inserts a text box in the GeoGebra drawing pad for inputs.
	Pen Tool	Enables writing/drawing on the drawing pad.
	Point on Object	Creates a point on a region or a perimeter of a region.
	Polyline	Creates a series of segments.
	Probability Calculator	Computes/graphs different probability distributions.
	Rigid Polygon	Creates a polygon that you can translate or rotate, but can’t change its shape.

 

GeoGebra 4.0 has not only improved by adding additional tools and features, there are also 7 minor changes in the interface.

 

Seven “Minor” Changes in GeoGebra’s GUI

1. The Perspective Menu

The most obvious change when you open the GeoGebra 4.0 window is the addition of the Perspectives menu. This menu will let you to choose the type of Perspective (combination of windows) to show.

The Basic Geometry perspective, for example, only reveals a blank drawing pad and displays the basic tools with no drop down list of tools. The Table & Graphics perspective shows the Spreadsheet View and a blank drawing pad.

Note: GeoGebra has changed the term “drawing pad” to Graphics View to be consistent with Algebra and Spreadsheet Views. From now on, we will use the term Graphics View in lieu of drawing pad.

2. Sort Object by Type

Another small improvement (which I really like very much) is the Sort Object by Type toggle button in the Algebra window. This enables you to sort the objects into two types — the first is to three categories:  Free, Independent, and Auxiliary Objects, and the other one is to sort into object types: Line, Segments,Number, Point, etc (see Figure 1).

3. Styling Bar

Thank goodness because we don’t have to right click or double click an object and open the Properties window when we want to change the color, style, size, or label type of a particular object.

In GeoGebra 4.0, a new styling bar is located at the top of the Graphics view. It can be shown/hidden using a toggle button discussed in number 4.

4. Action Buttons

I am not sure if the GeoGebra team has given a name for these three buttons (I can’t find it), but for now we will call them Action Buttons. The first one on the left is the Toggle Styling Bar button which shows/hides the Styling Bar. The second is the Show View in New Window button which lets the current window float.  The third one with the x is of course, the Close button.

5. The Greek Letters Window

The very long drop down list of Greek letters in version 3.2 is now in tabular form.

This is a great improvement because we don’t have to do a lot of mouse scrolling.

6. The Command History

The command history is also improved. In the last version, you have to press the UP arrow key on your keyboard to view the previous inputs from the input bar, but in version 4.0, you just have to click the up button to show the list.

7. Input Help

The GeoGebra commands are more organized. They are now sorted into categories and not just listed alphabetically. We can use the Input Help toggle button as shown in Figure 1 to display the list of commands, then we can do the 4-step instruction below to use the command below.

 

The Text tool was hard to use in GeoGebra 3.2. When you want to combine dynamic and static texts, you have to type confusing codes which include symbols such as the plus sign and double quotes.

GeoGebra 4.0, however, has a much improved Text tool.  In the new version, the name of each object can bee seen in the Objects drop down list (see Figure 1) on the Text tool dialog box. The values of these objects can be inserted  in a phrase/sentence by clicking them  on the list. After selecting a particular object, it’s name will be shown  in the Edit window (see Figure 2), while its value will be shown in the Preview window.  This saves us from writing variables, double quotations, and plus signs manually.

The big problem of the Object list, however, is when you have constructed a lot objects.  This will give you a very long list, and you will have to do a lot of scrolling down to look for a particular object.  I hope that this could also be improved later, in GeoGebra 5.0 perhaps, if it is not possible in the next version.

Another improvement in GeoGebra 4.0 is it has more math symbols. The symbols were also more organized in the new version.

The long wait is over. GeoGebra 4.0 can now graph inequalities as shown in Figure 1.

You can construct the graph above by typing the following in the Input bar pressing the ENTER key after each inequality.

 

1. y < 3x
2.  2x -1 <= 2
3.  y > x³ - 2x - 1

The symbol <= can also be found on the symbol box as ≤.  Just click the input bar and click the α symbol at the rightmost part of the input bar.

When we talk about inequalities, we talk about solutions. In GeoGebra 4.0, we can graph the solution of the three or more inequalities above using logical operators such as and (denoted by ∧). The graph shown in Figure 2 is the graph of the inequality  (-x + y ≤ 3) ∧ (4x + 3y < 12) ∧ (-x – 2y < -2).

The inequality is a new feature in GeoGebra is not yet stable. The logical operators might still have problems with functions with degree more than one. I used the logical operator on the first three inequalities, which include one quadratic inequality, but no output graph was shown.

One of the major enhancements of GeoGebra 4.0 is the integration of Computer Algebra System (CAS).  The GeoGebra CAS window can be viewed by clicking the View>CAS from the menu bar. The CAS toolbar includes the following tools as shown in the first figure: 

Evaluate	exact evaluation
Numeric	numeric evaluation; e.g. sin(1)
Keep Input
Factor
Expand
Substitute
Solve
Differential/ Integral

 

You can enter  expressions/equations at the CAS window (see black texts below) and click the buttons at the toolbar to perform a command. The output of a command is shown in blue texts. Line 1, for example, used the Evaluate button to simplify 2x + 4x – 3y + 2y.

The GeoGebra CAS also accepts keyboard input; type the command and then the expression. For example, typing solve[x^2 -3x + 5 = 10, x] in the CAS window is just the same as typing the equation  x^2 -3x + 5 = 10 and then clicking the Solve button.

For more information about the GeoGebra CAS commands and their syntax, read the GeoGebraCAS documentation.

The Function Inspector is a new tool introduced in GeoGebra 4.0.  This tool ‘inspects’ functions revealing properties such as its minima,  maxima, root, area, and mean, etc., of a given interval.

The Function Inspector can also generate tables  of values of  x and f(x) given an interval and step value. This is very useful since we do not have to type them manually and use formulas in the Spreadsheet View.  In addition to the x, f(x) table of values, we can also add columns that display the differences between consecutive f(x) values, first derivative, and the second derivative.

The Function Inspector can also generate tangent lines and osculating circle through a particular point on the graph of the function.