# GeoGebra Help Official Manual 3.2

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1 GeoGebra Help Official Manual 3.2 Markus Hohenwarter and Judith Hohenwarter

2 GeoGebra Help 3.2 Last modified: April 22, 2009 Authors Markus Hohenwarter, Judith Hohenwarter, GeoGebra Online: 2

3 Contents 1. WHAT IS GEOGEBRA? Multiple Views for Mathematical Objects Graphics View Algebra View Spreadsheet View GeoGebra as a Tool for Teaching and Learning Mathematics Customizing the User Interface The Properties Dialog The Context Menu GeoGebra as a Presentation Tool The Navigation Bar The Construction Protocol Customize the Settings GeoGebra as an Authoring Tool Printing Options Creating Pictures of the Graphics View Creating Interactive Webpages GEOMETRIC INPUT General Notes Construction Tools General Tools Point Tools Vector Tools Segment Tools Ray Tool Polygon Tools Line Tools Conic Section Tools Arc and Sector Tools Number and Angle Tools Boolean Variable Tool Locus Tool Geometric Transformation Tools Text Tool Image Tool ALGEBRAIC INPUT General Notes Direct Input

4 Numbers and Angles Points and Vectors Lines and Axes Conic Sections Functions of x Pre defined Functions and Operations Boolean Variables and Operations List Objects and Operations Matrix Objects and Operations Complex Numbers and Operations Commands General Commands Boolean Commands Number Commands Angle Command Point Commands Vector Commands Segment Command Ray Command Polygon Command Line Commands Conic Section Commands Function Commands Parametric Curve Command Arc and Sector Commands Text Commands Locus Command List and Sequence Commands Geometric Transformation Commands Statistics Commands Spreadsheet Commands Matrix Commands MENU ITEMS File Menu Edit Menu View Menu Options Menu Tools Menu Window Menu Help Menu SPECIAL GEOGEBRA FEATURES Animation Automatic Animation Manual Animation

5 5.2. Conditional Visibility User Defined Tools Dynamic Colors JavaScript Interface Keyboard Shortcuts Labels and Captions Layers Redefine Trace and Locus INDEX

6 1. What is GeoGebra? GeoGebra is dynamic mathematics software that joins geometry, algebra and calculus. It is developed for learning and teaching mathematics in schools by Markus Hohenwarter and an international team of programmers Multiple Views for Mathematical Objects GeoGebra provides three different views of mathematical objects: a Graphics View, a, numeric Algebra View, and a Spreadsheet View. They allow you to display mathematical objects in three different representations: graphically (e. g., points, function graphs), algebraically (e. g., coordinates of points, equations), and in spreadsheet cells. Thereby, all representations of the same object are linked dynamically and adapt automatically to changes made to any of the representations, no matter how they were initially created. Toolbar Toolbar Help Algebra View Spreadsheet View Graphics View Input Bar Graphics View Using the construction tools available in the Toolbar you can do geometric constructions in the Graphics View with the mouse. Select any construction tool from the Toolbar and read the Toolbar Help (next to the Toolbar) in order to find out how to use the selected tool. Any object you create in the Graphics View also has an algebraic representation in the Algebra View. 6

7 Note: After activating the tool Move you are able to move objects in the Graphics View by dragging them with the mouse. At the same time, their algebraic representations are dynamically updated in the Algebra View. Every icon in the Toolbar represents a toolbox that contains a selection of similar construction tools. In order to open a toolbox, you need to click on the small arrow in the lower right corner of the Toolbar icon. Hint: Construction tools are organized by the nature of resulting objects or the functionality of the tools. You will find tools that create different types of points in the Point Toolbox (default icon ) and tools that allow you to apply geometric transformations in the Transformation Toolbox (default icon ) Algebra View Using the Input Bar you can directly enter algebraic expressions in GeoGebra. After hitting the Enter key your algebraic input appears in the Algebra View while its graphical representation is automatically displayed in the Graphics View. Example: The input f(x) = x^2 gives you the function f in the Algebra View and its function graph in the Graphics View. In the Algebra View, mathematical objects are organized as free and dependent objects. If you create a new object without using any other existing objects, it is classified as a free object. If your newly created object was created by using other existing objects, it is classified as a dependent object. Hint: If you want to hide the algebraic representation of an object in the Algebra View, you may specify the object as an auxiliary object: Right click (Mac OS: Ctrl click) on the corresponding object in the Algebra View and select Properties from the appearing Context Menu. On tab Basic of the Properties Dialog you may specify the object as an Auxiliary Object. By default, auxiliary objects are not shown in the Algebra View, but you can change this setting by selecting the item Auxiliary Objects from the View menu. Note that you are able to modify objects in the Algebra View as well: Make sure that you activate the Move tool before you double click on a free object in the Algebra View. In the appearing text box you can directly edit the algebraic representation of the object. After hitting the Enter key, the graphical representation of the object will automatically adapt to your changes. If you double click on a dependent object in the Algebra View, a dialog window appears allowing you to Redefine the object. GeoGebra also offers a wide range of commands that can be entered into the Input Bar. You can open the list of commands in the right corner of the Input Bar by clicking on the button Command. After selecting a command from this list (or typing its name directly into the Input Bar) you can press the F1 key to get information about the syntax and arguments required to apply the corresponding command. 7

15 Note: If the size of your applet is too big to fit on a computer screen with standard resolution (1024 x 768), you may want to resize it before the actual export as a Dynamic Worksheet. Note: Several files are created when you export a Dynamic Worksheet: HTML file (e. g. circle.html) this file includes the worksheet itself GGB file (e. g. circle.ggb) this file includes your GeoGebra construction JAR (several files) these files include GeoGebra and make your worksheet interactive All these files (e. g. circle.html, circle.ggb and the geogebra.jar files) have to be in one folder (directory) to let the dynamic construction work. The exported HTML file (e. g. circle.html) can be viewed with any Internet browser (e. g. Mozilla, Internet Explorer, Safari). In order to let the dynamic construction work, Java has to be installed on the computer. You can get Java from without charge. If you want to use your Dynamic Worksheet in your school's computer network, ask your local network administrator to install Java on the computers. Note: You can edit the Dynamic Worksheet's text with many word processing systems (e. g. FrontPage, OpenOffice Writer) by opening the exported HTML file. You may also edit the Dynamic Worksheet's applet by opening the GGB file in GeoGebra and saving it with the same name afterwards. 15

16 2. Geometric Input 2.1. General Notes The Graphics View shows the graphical representation of mathematical objects (e. g., points, vectors, segments, polygons, functions, curves, straight lines, conic sections). Whenever the mouse is moved over one of these objects a description appears as a rollover text and the object is highlighted. There are several tools/modes to tell GeoGebra how it should react to mouse input in the Graphics View (see section Construction Tools). For example, clicking on the drawing pad can create a new point (see tool New Point), intersect two objects (see tool Intersect Two Objects), or create a circle (see Circle tools) Construction Tools The following construction tools or modes can be activated by clicking on the buttons of the Toolbar. You can click on the small arrow in the lower right corner of an icon to open a Toolbox with similar other tools. Note: With most construction tools you can easily create new points by clicking on empty spaces on the drawing pad. Selecting Objects To select an object means to click on it with the mouse after selecting the Move tool. If you want to select several objects at the same time, you could draw a selection rectangle: Select the Move tool and click on the position of the first corner of your desired selection rectangle. Hold the left mouse key pressed down and move the pointer to the position of the diagonally opposite corner of your desired selection rectangle. After releasing the mouse button, all objects within the selection rectangle are selected. Note: By holding the Ctrl key (Mac OS: Cmd key) while clicking on different objects, you can select several objects at the same time. Fast Renaming of Objects To quickly rename a selected or newly created object just start typing to open the Rename dialog for this object. Then, type in the new name of the selected object and click on the OK button. 16

17 General Tools Copy Visual Style This tool allows you to copy visual properties (e. g., color, size, line style) from one object to one or more other objects. To do so, first select the object whose properties you want to copy. Then, click on all other objects that should adopt these properties. Delete Object Click on any object you want to delete (also see command Delete). Note: You can use the Undo button if you accidentally deleted the wrong object. Move Drag and drop free objects with the mouse. If you select an object by clicking on it in Move mode, you may delete the object by pressing the Delete key move the object by using the arrow keys (see section Manual Animation) Note: You can quickly activate the Move tool by pressing the Esc key of your keyboard. Move Drawing Pad Drag and drop the drawing pad in the Graphics View to change its visible area. Note: You can also move the drawing pad by pressing the Shift key (MS Windows: also Ctrlkey) and dragging it with the mouse in any mode. In this mode you can also scale each of the axes by dragging it with the mouse. Record to Spreadsheet This tool allows you to move an object and to record a sequence of its values in the Spreadsheet View. This tool works for numbers, points, and vectors. Note: GeoGebra will use the first two empty columns of the Spreadsheet View to record the values of the selected objects. Relation Select two objects to get information about their relation in a pop up window (also see command Relation). 17

18 Rotate around Point Select the center point of the rotation first. Then, you may rotate free objects around this point by dragging them with the mouse (also see command Rotate). Show / Hide Label Click on an object to show or hide its label. Show/Hide Object Select the object you want to show or hide after activating this tool. Then, switch to another tool in order to apply the visibility changes to this object. Note: When you activate this tool, all objects that should be hidden are displayed in the Graphics View highlighted. In this way, you can easily show hidden objects again by deselecting them before switching to another tool. Zoom In Click on any place on the drawing pad to zoom in (also see section Customizing the Graphics View). Note: The position of your click determines the center of zoom. Zoom Out Click on any place on the drawing pad to zoom out (also see section Customizing the Graphics View). Note: The position of your click determines the center of zoom Point Tools Intersect Two Objects Intersection points of two objects can be created in two ways (also see command Intersect). Selecting two objects creates all intersection points (if possible). Directly clicking on an intersection of the two objects creates only this single intersection point. Note: For segments, rays, or arcs you may specify whether you want to Allow outlying intersections on tab Basic of the Properties Dialog. This can be used to get intersection points that lie on the extension of an object. For example, the extension of a segment or a ray is a straight line. 18

19 Midpoint or Center You may click on either two points or one segment to get its midpoint. You can also click on a conic section (circle or ellipse) in order to create its center point (also see commands Center and Midpoint). New Point Click on the drawing pad in the Graphics View in order to create a new point. The coordinates of the point are fixed when the mouse button is released. Note: By clicking on a segment, straight line, polygon, conic section, function, or curve you can create a point on this object (also see command Point). Clicking on the intersection of two objects creates this intersection point (also see tool Intersect Two Objects and command Intersect) Vector Tools Vector between Two Points Select the starting point and then the end point of the vector (also see command Vector). Vector from Point Select a point A and a vector v to create the new point B = A + v as well as the vector from A to B (also see command Vector) Segment Tools Segment between Two Points Select two points A and B in order to create a segment between A and B (also see command Segment). Note: In the Algebra View, the segment's length is displayed. Segment with Given Length from Point Click on a point A that should be the starting point of the segment. Specify the desired length a of the segment in the appearing window (also see command Segment). Note: This tool creates a segment with length a and endpoint B which may be rotated around the starting point A by using tool Move. 19

20 Ray Tool Ray through Two Points Selecting two points A and B creates a ray starting at A through B (also see command Ray). Note: In the Algebra View the equation of the corresponding line is displayed Polygon Tools Polygon Successively select at least three points which will be the vertices of the polygon. Then, click the first point again in order to close the polygon (also see command Polygon). Note: In the Algebra View, the polygon's area is displayed. Regular Polygon Select two points A and B and specify the number n of vertices in the text field of the appearing dialog window. This gives you a regular polygon with n vertices including points A and B (also see command Polygon) Line Tools Angle Bisector Angle bisectors can be defined in two ways (also see command AngleBisector): Selecting three points A, B, and C produces the angle bisector of the enclosed angle, where point B is the apex. Selecting two lines produces their two angle bisectors. Note: The direction vectors of all angle bisectors have length 1. Best Fit Line Create the best fit line for a set of points in the following ways (also see command FitLine): Create a selection rectangle that contains all points. Select a list of points to create their corresponding best fit line. Line through Two Points Selecting two points A and B creates a straight line through A and B (also see command Line). Note: The line s direction vector is (B A). 20

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