GeoGebra Exam Mode

The new GeoGebra Exam Mode allows you and your students to use the power of GeoGebra during exams alongside paper and pencil (ie like a graphing calculator) while restricting their access to the Internet and other software on their computers that should not be used during the exam.

GeoGebra Exam

The GeoGebra Exam Mode …

  • can be easily accessed at
  • runs in your browser (e.g. Chrome, Firefox, Internet Explorer 11, Safari), so no additional installations are required
  • can be customized in case your students should not have access to the full power of GeoGebra, eg you can turn off CAS or 3D features for exams
  • runs in fullscreen mode so students can’t use other programs or files during an exam

If a student leaves the GeoGebra Exam window (eg by opening another browser tab), the top header of GeoGebra Exam turns red immediately. An information button shows the Exam Log with detailed information when that happened and for how long.

GeoGebra Exam Alert

GeoGebra Exam Log

For more details on how to best use the GeoGebra Exam Mode during tests and exams, please see our GeoGebra Exam Tutorial. We plan to include the Exam Mode in our offline apps (Chrome, tablet, phone) as well soon. For now, please give it a try and let us know any ideas for improvements at, thanks!

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GeoGebra Graphing Calculator Released

We’re pleased to announce the first public release of our GeoGebra Graphing Calculator! It’s for Android phones and tablets right now, iPhone and Windows will follow, watch this space!

For the first release it has the graphics and algebra views but we will be adding lots more features over the coming months. We have prepared the foundations so everything necessary is already working under-the-hood (for example the CAS engine, and you can create – but not yet display – 3D objects).

There are also some extra-cool goodies to enjoy:

  • brand-new native equation editor
  • long-tap on an object to change its properties
  • drag sliders and animate them in the Algebra View
  • freehand drawings and shape recognition
  • everything is running natively (LaTeX, CAS, graphics drawing etc) so it is super-slick to use
  • search, open and save from/to GeoGebraTube
  • find out more in our tutorial Graphing Calculator Tutorial

Graphing Search Materials Geometry

You can download it in the Play Store now for Android phones and tablets – please let us know your ideas for improvements with the “Send Feedback” option or in our Mobile Apps forum.

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GeoGebra Groups – Collaboration for Everyone

The GeoGebra community is all about creating and sharing great materials for learning math & science. Thanks to you, we now have more than 300,000 free and interactive worksheets and books.

But wouldn’t it be nice to also hear back from your students or colleagues who you shared your materials with? We think so too! That’s why we have created GeoGebra Groups:

  • Supercool and easy collaboration between students and teachers, colleagues, and really just everyone nice out there!
  • Invite others using your Group Code
  • Post texts, images, videos, pdfs and GeoGebra worksheets to your Group
  • Add questions and interactive GeoGebra tasks for your students and give them feedback
  • Discuss your ideas with everyone or individual Group members using comments
  • Find out how to do all that and more in our GeoGebra Groups Tutorial

Try out our Groups, start to collaborate in a new way, and let us know what you think!





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GeoGebra for Phones Beta

We’re pleased to announce the first public beta-release of GeoGebra for Android Phones. We’ve already started on an iPhone app, watch this space!

For the first release it will have just the Graphics View and Algebra View but we will be adding lots more features over the coming months. We have prepared the foundations already so everything necessary is already working under-the-hood (for example the CAS engine, and you can create – but not yet display – 3D objects).

There are also some extra-cool phone-only goodies to enjoy:

  • brand-new native equation editor
  • shake your phone to update random numbers (coming soon!)
  • freehand drawings and shape recognition
  • long-tap on an object to change its properties
  • drag sliders and animate them in the Algebra View
  • everything is running natively (LaTeX, CAS, graphics drawing etc) so it is super-slick to use

You can download it in the Play Store now (for Android phones and tablets!) – please let us know what you think with the “Send Feedback” option.

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My World My Math!

Here’s a few things we really like in our world at GeoGebra:

  1. Our community… yes, YOU 🙂
  2. Our partners, and, last but not least …
  3. Mathematics!

So we got together with a few amazing members of our community, one really awesome partner, and then turned the cameras ON. With a little fancy footwork, cutting, pasting… Voila!

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Google Summer of Code 2015

GeoGebra Summer of Code 2015

This summer, GeoGebra was again part of Google Summer of Code (GSoC) supporting young and talented open source coders. We had a very strong field of 64 students applying and were able to choose 4 of them to work with us during this summer. There were also some impressive contributions submitted by many of the other candidates which have already been incorporated into GeoGebra.

Yi-Chun (Jacky) Kuo: Native iOS App



Our current iPad app is based on a WebView so we were interested to see if Jacky could make a prototype of a native app using the quite-new RoboVM cross-compiler to convert GeoGebra’s Java code into Objective C. As part of his application he managed to get the JLaTeXMath formula engine working which was very impressive in its own right. For the first half of his project he got the full GeoGebra kernel compiled and running and for the second half he worked on drawing objects and user-interaction.

There is still a lot to do before we can make a release (for example implementing the toolbar and equation editor) but Jacky will stay on with GeoGebra after GSoC to help!


GeoGebra running in Xcode

Georgios Ouzounis: Handwritten Equation Recognition



Image showing handwritten 6x^4 + sqrt of 7x over 8+x = 4y^3 recognized and converted to an equation

Handwritten equation recognized!

Georgios made a nice web app as part of his application to collect example handwritten equations from phones and tablets and store them in a database. This was important as it allowed him to use that data when testing and training his algorithms. The three parts to his project were:

  • splitting the equation into its symbols
  • recognising the symbols
  • converting that back into GeoGebra syntax

and by the end of his project it was successfully recognizing indices, fractions and square-roots. At the moment the code is running server-side and is a little slow so the challenge for the future will be to get it running faster and client-side. Open Source libraries used: OpenCV

Thilina Madumal: Intersection Project


Polygon Intersections in 2D and 3D

Polygon Intersections in 2D and 3D!

As part of Thilina’s application, he adapted the Clipper library to compile with Java 6 and with GWT and incorporated it into GeoGebra, which he then used as part of his main GSOC project to improve the polygon operations within GeoGebra.

He has also done a lot of work on improving the Intersect command to allow the intersection of many more object types to be calculated dynamically.

Shamshad Alam: Implicit Curves Project


Family of curves cos(x y) = k

cos(x y) = k

3D plot of x^4+y^4+z^4=2

x^4 + y^4 + z^4 = 2

Polygon shown with an extra thin "path" drawn all the way round the outside

Shamshad also made some nice experiments with the Clipper library as part of his application

The main focus of his GSoC project was to implement plotting of implicit curves and surfaces, namely:

  • plotting of non-polynomial implicit curves (for example you can try sin(x) – sin(y) = 1 in GeoGebra Beta)
  • plotting of implicit surfaces (eg x⁴ + y⁴ + z⁴ = 2)
  • extending commands for rotation, translation and other transformations to work with these object types

Thanks to all our GSoC students for a great job done during this summer!

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New Equation Editor and Keyboard

We’ve made some nice changes to our Chrome, Web and Tablet apps recently that many of you have been asking for. The first exciting feature is that the Input Bar in the Algebra View has expanded into a fully-fledged Equation Editor, for example:


and it also works fully with GeoGebra commands:


It’s now also much easier to add and edit matrices, parametric curves and piecewise-defined functions:


We’ve also added a touch-friendly on-screen keyboard that supports many languages and works nicely with our new equation editor:


You can try these cool new features in any of our web and tablet apps!

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Fast, Beautiful LaTeX comes to GeoGebraTube

We’ve made a major change to GeoGebraTube and our Chrome App. We have updated the formula renderer (otherwise known as LaTeX renderer) to use the same version as in the desktop version. This means that mathematical formulas in our applets and web application will now look just as beautiful as they do in GeoGebra’s desktop version. This will work with all existing formula commands as well (for example TableText, FormulaText, FractionText, StemPlot).



Here’s an example of the new version using our new super-pretty formulas:

If you have any questions or suggestions concerning these new updates, please write to us at

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GeoGebra Global Gathering

We are happy to inform you that the official registration and abstract submission for the GeoGebra Global Gathering Conference are now open.

Join us at our GeoGebra Global Gathering (G3, 2015) July 15 – 17 in Linz in Austria and register now!

Because there is only a limited number of participants we can host, we highly recommend to register for our gathering as soon as possible to make sure you can join us this July. Please find more information about all the practicalities in our G3 2015 GeoGebraBook.

We are looking forward to seeing you this summer in Linz!
Markus and the GeoGebra Team

GeoGebra Global Gathering 2015

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Volume of Pyramids with GeoGebra

“That which is provable, ought not to be believed in science without proof,” said Richard Dedekind.  The formula for the volume of a pyramid is usually learnt in junior forms without any proof.  One may think that such proofs require calculus.  In fact the formula was well known before the invention of calculus.  If we look back to the history, we can find some explanations and proofs which are comprehensible to lower form students.  These proofs are more accessible with the use of the dynamic GeoGebra 3D figures.

The following approach of deriving the formula for volume of a pyramid was reported to be originated from Democritus (Edwards 1979, p.8-10).  In the first figure below, a red triangular pyramid is “completed” to form a prism together with the blue and the green pyramids.  Check each of the boxes and drag the blue slider, we can see that the red and the blue pyramids, and also the blue and the green pyramids, always have equal sections at equal heights (the 2nd and the 3rd figures below).  Considering that a pyramid is composed of sections parallel to its base, the red pyramid and the blue pyramid are then equal in volumes, and so are the blue and the green pyramids (Cavalieri’s principle). Since the three pyramids composing the prism are equal in volumes, the volume of the red pyramid is therefore one-third of that of the prism, and hence one-third of its base area times the height.
pyramid_Screenshot_1  pyramid_Screenshot_2  pyramid_Screenshot_3
(Click here to access the dynamic figure.)

It is worthwhile to note that a Chinese mathematician LIU Hui (劉徽, fl. 3rd century) proved the result in an ingenious way.  In his commentary of the Chinese’s mathematical classics “Arithmetic in Nine Chapters (九章算術)”, the triangular prism is divided into a triangular pyramid and a rectangular pyramid (the 1st figure below).  After pressing the “Start” and then the “Next” button, with the midpoints of the edges each of the pyramids are divided into some prisms (the red and yellow parts) and some empty smaller pyramids. It is clear that the sum of the volumes of the red parts is half of that of the yellow parts (the 2nd figure below).
pyramid_Screenshot_4 pyramid_Screenshot_5
(Click here to access the dynamic figure.)

The smaller pyramids can be further divided up accordingly (press the “Next” button again to see). Again the sum of the volumes of the red parts is half of that of the yellow parts. The same process can be continued indefinitely (press the “Next” button repeatedly) and we shall see that the limiting shapes, the red triangular pyramid and the yellow rectangular pyramid, have the ratio 1 : 2 in volumes. Therefore the volume of the red triangular pyramid is one-third of that of the prism, and hence the result.
pyramid_Screenshot_6 pyramid_Screenshot_7
pyramid_Screenshot_8 pyramid_Screenshot_9
(Click here to access the dynamic figure.)

LIU Hui expressed his idea of carrying the process to the limit as follows (Wagner, 1979):
The smaller they are halved, the finer are the remaining. The extreme of the fineness is called “subtle”. That which is subtle is without form. When it is explained in this way, why concern oneself with the remainder?
It is particularly impressive that LIU Hui could visualize this subtle limit process, as illustrated by the above dynamic figure, without the help of modern technology.

The above two applets are also available in the GeoGebraBook:


Edwards, C. H. Jr. 1979. The Historical Development of the Calculus. Springer-Verlag, New York

Wagner, D.B. 1979. An Early Chinese Derivation of the Volume of a Pyramid: Liu Hui, Third Century A.D. Historia Mathematica 6 p.164-188

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