About
Geogebra is open source mathematics software free to use,modify and distribute.It is classified as an "Interactive Geometry Software"(IGS) also called "Dynamic Mathematics Software".A typical Dynamic geometry software lets users create geometrical figures(mostly 2D) and manipulate them,while dynamically changing their attributes and dependent objects(e.g. moving a line to move a point or changing area of a polygon by moving the vertices).Other similar IGS are C.A.R,CarMetal,DrGeo.
Along with creation and manipulation of all geometric constructs in 2 D plane,Geogebra also simplifies explanation of geometry through algebraic equations for each geometric construction.It also provides curves and graphs for calculus functions like sine,cos,tan,derivative,Integral for fairly complex equations.So Geogebra combines the three parts of Mathematics-Geometry,Algebra and Calculus.
How and where you can use it?
Geogebra's primary usability comes with its ability to represent an object in both its geometric and algebraic form.Most of high school and secondary school geometry can be taught with the help of this combined functionality.Algebraic equations and their solutions can be explained by showing their geometric curves,and geometric constructions can be done by using their algebraic equations.Since there is also rich pool of trigonometric functions like sine,cos,tan and calculus functions like derivative,integral etc. complex calculus equations can be explained using their geometric curves.You can use it as a drawing board while teaching or explaining a the concept or solving a problem,or you can use pre-authored pictures(png,vector graphics images) or construction steps,or you can use it for creating dynamic html applets.
Using Geogebra as Drawing Board
Geogebra can be used for creating all geometrical constructs like points,lines,polygons and manipulate them.It provides a rich GUI with common objects like point,line segment, mid-point ,vector,perpendicular-bisector,angle-bisector,angle-measure,length measurement etc. in simple drop-down menus.You can create most figures of
text book easily and show changes or geometrical properties and theorems on drawing board itself.
For instance you may show how all points on angle bisector are equidistant from lines forming the angle by drawing two lines forming an angle,measure angle between them,drawing its angle-bisector,marking points on this bisector and measuring perpendicular distance from lines.
Objects attributes like color, line style, label etc. can be changed to differentiate or highlight different objects.You can also zoom-in,zoom-out,pan or modify the axes and grid.More complex figures like "family of line/circles" and trigonometric function graphs like sine,cos,sec,tan,cot etc. can be also made using simple command interface.
A student may also be given this to play around with,and complete a task.You can use it to give student exercises like draw triangle of certain dimensions and then draw its circumcircle or find its centroid, verify the property of division of median by centroid or other similar exercises.The student would submit saved geogebra files(.ggb files) and you can run it on your system in geogebra and check the way he constructed it by playing constructions steps.
Using Geogebra Created Static or Dynamic Content
Geogebra can be used to create static pictures or dynamic web applets to be used in other platforms.Pictures of the figures drawn on drawing board can be exported to formats embeddable in a word,html etc. documents.Static pictures can then be modified in image processing tools,
You can create a solution figures yourself or use a pre-created worksheet,pictures to present students.There is big pool of contributed geogebra files and worksheets on geogebra wiki and forum.These are uploaded files and dynamic html pages which can be show using presentation tools.
A few examples of how geogebra created dynamic worksheets can be used
1. Showing construction steps using "Navigation Bar for construction steps" as done here.
Navigation bar for construction steps is as easy to use as a player.This can be used by teacher or given to students to parse through each step of geometric construction.
2. Hiding and showing objects or areas on the x-y plane using "checkboxes" as done here.
Checkboxes can be included in view and linked to one or more objects to control their visibility.This simple interaction can be useful in showing/hiding particular objects to demonstrate overlapping graphs,or "simultaneous equations".
3. Moving an object or point on the view page,and dynamically changing other objects and changing variable values using slider.
Can be used to show how geometric objects/curves change with changing variables.A slider can
be used as input of values.This can be used to explain when one object depends on other objects or variables, e.g. how conics change with "eccentricity",proving or verifying theorems.
Creating an dynamic worksheet like the ones above is often obviated by the large pool of contributed worksheets but creating them too requires little effort.The objects like slider,navigation bar for construction,check boxes and figures can be constructed from the drop-down menu and command menu,then entire geogebra file can be exported to dynamic worksheet which can be displayed on any java enabled browser or embedded in webpage.
Where you can get it from?
1. Official Geogebra website
2. Geogebra wiki
License
Geogebra is available under GNU-GPL. Most of the supporting content like contributed worksheets, and tutorials are available under CC by NCSA(Creative commons by Non commercial share-alike).
Useful Links
A comprehensive introduction can be found at official geogebra introduction page,easier user manual and video tutorial on youtube.
Geogebra is open source mathematics software free to use,modify and distribute.It is classified as an "Interactive Geometry Software"(IGS) also called "Dynamic Mathematics Software".A typical Dynamic geometry software lets users create geometrical figures(mostly 2D) and manipulate them,while dynamically changing their attributes and dependent objects(e.g. moving a line to move a point or changing area of a polygon by moving the vertices).Other similar IGS are C.A.R,CarMetal,DrGeo.
Along with creation and manipulation of all geometric constructs in 2 D plane,Geogebra also simplifies explanation of geometry through algebraic equations for each geometric construction.It also provides curves and graphs for calculus functions like sine,cos,tan,derivative,Integral for fairly complex equations.So Geogebra combines the three parts of Mathematics-Geometry,Algebra and Calculus.
How and where you can use it?
Geogebra's primary usability comes with its ability to represent an object in both its geometric and algebraic form.Most of high school and secondary school geometry can be taught with the help of this combined functionality.Algebraic equations and their solutions can be explained by showing their geometric curves,and geometric constructions can be done by using their algebraic equations.Since there is also rich pool of trigonometric functions like sine,cos,tan and calculus functions like derivative,integral etc. complex calculus equations can be explained using their geometric curves.You can use it as a drawing board while teaching or explaining a the concept or solving a problem,or you can use pre-authored pictures(png,vector graphics images) or construction steps,or you can use it for creating dynamic html applets.
Using Geogebra as Drawing Board
Geogebra can be used for creating all geometrical constructs like points,lines,polygons and manipulate them.It provides a rich GUI with common objects like point,line segment, mid-point ,vector,perpendicular-bisector,angle-bisector,angle-measure,length measurement etc. in simple drop-down menus.You can create most figures of
text book easily and show changes or geometrical properties and theorems on drawing board itself.
For instance you may show how all points on angle bisector are equidistant from lines forming the angle by drawing two lines forming an angle,measure angle between them,drawing its angle-bisector,marking points on this bisector and measuring perpendicular distance from lines.
Objects attributes like color, line style, label etc. can be changed to differentiate or highlight different objects.You can also zoom-in,zoom-out,pan or modify the axes and grid.More complex figures like "family of line/circles" and trigonometric function graphs like sine,cos,sec,tan,cot etc. can be also made using simple command interface.
A student may also be given this to play around with,and complete a task.You can use it to give student exercises like draw triangle of certain dimensions and then draw its circumcircle or find its centroid, verify the property of division of median by centroid or other similar exercises.The student would submit saved geogebra files(.ggb files) and you can run it on your system in geogebra and check the way he constructed it by playing constructions steps.
Using Geogebra Created Static or Dynamic Content
Geogebra can be used to create static pictures or dynamic web applets to be used in other platforms.Pictures of the figures drawn on drawing board can be exported to formats embeddable in a word,html etc. documents.Static pictures can then be modified in image processing tools,
You can create a solution figures yourself or use a pre-created worksheet,pictures to present students.There is big pool of contributed geogebra files and worksheets on geogebra wiki and forum.These are uploaded files and dynamic html pages which can be show using presentation tools.
A few examples of how geogebra created dynamic worksheets can be used
1. Showing construction steps using "Navigation Bar for construction steps" as done here.
Navigation bar for construction steps is as easy to use as a player.This can be used by teacher or given to students to parse through each step of geometric construction.
2. Hiding and showing objects or areas on the x-y plane using "checkboxes" as done here.
Checkboxes can be included in view and linked to one or more objects to control their visibility.This simple interaction can be useful in showing/hiding particular objects to demonstrate overlapping graphs,or "simultaneous equations".
3. Moving an object or point on the view page,and dynamically changing other objects and changing variable values using slider.
Can be used to show how geometric objects/curves change with changing variables.A slider can
be used as input of values.This can be used to explain when one object depends on other objects or variables, e.g. how conics change with "eccentricity",proving or verifying theorems.
Creating an dynamic worksheet like the ones above is often obviated by the large pool of contributed worksheets but creating them too requires little effort.The objects like slider,navigation bar for construction,check boxes and figures can be constructed from the drop-down menu and command menu,then entire geogebra file can be exported to dynamic worksheet which can be displayed on any java enabled browser or embedded in webpage.
Where you can get it from?
1. Official Geogebra website
2. Geogebra wiki
License
Geogebra is available under GNU-GPL. Most of the supporting content like contributed worksheets, and tutorials are available under CC by NCSA(Creative commons by Non commercial share-alike).
Useful Links
A comprehensive introduction can be found at official geogebra introduction page,easier user manual and video tutorial on youtube.
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