‫نظام جيوجيربا واستخداماته يف الرياضيات‬
‫ووسائل االيضاح املتحركة‬
GeoGebra: its uses in Mathematics and the Animated
illustrations
(Hands–on Sessions)
Dr. Thaer O. Roomi
Dr. Hussam T. Majeed
‫ واستخداماته في الرياضيات ووسائل‬Geogebra ‫نظام جيوجيبرا‬
‫االيضاح المتحركة‬
› What is GeoGebra?
› Installing GeoGebra.
› Add your third bullet point here
What is GeoGebra?
› GeoGebra is an application for exploring and demonstrating Geometry and Algebra.
› It is an open source application and is freely available for non-commercial use.
› It is available for many platforms: Windows, Mac, Linux
› It was created by Markus Hohenwarter in 2001/2002 as part of his master’s thesis in
mathematics education and computer science at the University of Salzburg in Austria.
› GeoGebra received many international awards.
› It was translated by mathematics teachers all over the world to more than 25 languages.
› Since 2006 GeoGebra is supported by the Austrian Ministry of Education to maintain the free
availability of the software for mathematics education at schools and universities.
› In July 2006, GeoGebra found its way to the US, where its development continues at Florida
Atlantic University.
Accessing GeoGebra
Webstart
Download
Pros
Up-to-date
Cons
Needs internet
Pros
Work Offline
Cons
Needs updates
› To start GeoGebra go to http://www.geogebra.org
› For Webstart : Use the Apps directly.
› For Download: click on App Downloads.
› GeoGebra includes many applications:
1.
Graphing Calculator: Graph functions, investigate equations, and plot data with our free graphing app
2.
3D Calculator: Graph 3D functions, plot surfaces and do 3D geometry with our free 3D Grapher
3.
Geometry: Construct circles, angles, transformations and more with our free geometry tool
4.
GeoGebra Classic 5: Apps bundle including free tools for geometry, spreadsheet, probability, and CAS
5.
GeoGebra Classic 6: Apps bundle including free tools for geometry, spreadsheet, probability, and CAS
6.
CAS Calculator: Solve equations, expand and factor expressions, find derivatives and integrals
For download…
Note: Pin the program into taskbar
Running GeoGebra 5
Launching
Double click the
GeoGebra icon on your
desktop to start the
application.
You will be presented
with a launch screen as
in the figure.
Clear Space
Input and commands
Buttons
Drawing Pad or
Graphics view
Running GeoGebra 6
Graphics view
Algebra view
Buttons for GeoGebra Toolbar
to select object and move it around the drawing area or to delete it
lets you either sketch a function, or you can draw a freehand circle, segment or
polygon and it will be recognized and converted to an exact shape.
Write or draw, you can change the color from style bar
Select position, line, function or curve
Select object or its perimeter to create a point, which is fixed to an object . Point included
Select point then object to attach. the point can still be moved via Move Tool , but only
within the path or region.
Select intersection or two objects successively . Move the intersection point !
Constructs the midpoint of a line segment or a center of an object
Creates a complex number
Select a function to find its extrema. Click on a function to find its local extrema
Select a function to find its roots. For example y=x^2 ->
(0,0)
Buttons for GeoGebra Toolbar
Select two points : draws an infinite line through two selected points.
Select two points : Draws a line segments between two selected points
Select point and enter segment length
Select starting point, then point on ray: draws a ray through two points
Select all vertices, then click first vertex again:
Select starting point, then end point
Vector from point: Select starting point and vector allows you to draw a
vector parallel to a given vector
Buttons for GeoGebra Toolbar
Select point and perpendicular line: draw a line perpendicular to a given line.
Select point and parallel line: draw a line perpendicular to a given line.
Select two points or one segment : used to bisect a line segment
Select three points or two lines: bisects a previously constructed angle
Draw tangents to a circle, a conic or the graph of a previously defined function
Select point or line then a circle or conic
Select points using selection rectangle or list of points.
Select locus point , then point on object or slider. Locus is a point with
a equidistance from two points
Buttons for GeoGebra Toolbar
Select all vertices then click first vertex again. allows you to construct a
closed polygon.
Select two points and enter number of vertices, allows you to draw a
regular polygon.
Select all vertices then click first vertex again (or just click on polygon
to make a rigid copy). It can rotate around one of the vortices
Select all vertices then click first vertex again. The resulting polygon will
keep the shape when the first point is dragged, but the other vertices can
be moved freely.
Buttons for GeoGebra Toolbar
Select center point, then point on circle. works by either clicking on the
point you want to be the center of the circle or clicking a blank space.
Select center point, and enter radius
Select segment or two points for radius. Try to change the center!
click on three different points. Circle through these points is constructed.
Click with it in two different places to construct the semicircle with that
line segment as diameter.
Click to construct center. Click and move anticlockwise to construct arc.
Select three points on arc.
Select center then two points.
Select three points on arc.
Buttons for GeoGebra Toolbar
Select two foci and a point on ellipse.
Select two foci and a point on hyperbola.
Select a point and a directrix.
Select five points on conic.
Buttons for GeoGebra Toolbar
Select two points or three lines. Direction is important !
Select leg point, vertex then enter size.
Select two points, a segment, a polygon, or a circle
Select polygon, circle or conic
Select line. You will get the slope.
Creates list of selected cells. Drag a rectangle around the objects you
wish to put in the list
Select two objects. It finds the relation between two objects
Select a function that you want to explore. The Function Inspector tool
can provide some information about the functions defined in algebra view.
Buttons for GeoGebra Toolbar
Select object to reflect , then line of reflection
Select object to reflect , then center point
Select object to reflect then circle to specify the mirror/circle of inversion.
Select object to rotate and center point, then enter angle
Select object to translate then vector.
Select object then center point then center factor