GeoGebra Math Apps for Desktop

Users on Tablets and our online GeoGebra App already have the advantage of our new slick user-interface. The good news is… we’ve now also updated our offline desktop apps for Windows, Mac and Linux. So, GeoGebra Math Apps now has the same touch-friendly and modern interface across all platforms!

Main improvements of the new GeoGebra Math Apps for desktop:

  • Same, great user-interface across all platforms and webpages
  • New full-featured equation editor in the Algebra View
  • Enhanced Algebra View (with sliders, checkboxes and exact fractions)
  • Enhanced Insert Image Tool to use with your WebCam
  • Saving integrated with your GeoGebra Account so you can access your files from all platforms
  • Offline installation and saving of .ggb files still supported, of course!

And for those of you who are happy with the good old GeoGebra Classic desktop versions: we will continue to support them with bug fix updates in the future as well.

You can get the new and shiny GeoGebra Math Apps for desktop and other platforms from beta.geogebra.org/download and the regular download page will be updated very soon.

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GeoGebra Graphing Calculator for iPhone

We’re pleased to announce the first public preview release of our GeoGebra Graphing Calculator for iPhones!

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 well so everything necessary is already working under-the-hood (for example the LaTeX formula engine, and you can create – but not yet display – 3D objects).

We will be making new releases each month so that it will soon catch up with the Android version.

There are also some extra-cool goodies to enjoy:

  • brand-new native equation editor
  • freehand drawings and shape recognition
  • everything is running natively so it is super-slick to use
  • find out more in our tutorial Graphing Calculator Tutorial

ios1 ios2 ios3

You can download it now in the App Store – please let us know which features we should add next in the GeoGebra Forums or send us an email: support@geogebra.org

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GeoGebra Exam Apps for Android Tablets and Chromebooks

The GeoGebra Exam Apps allow 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 that should not be used during the exam, see http://www.geogebra.org/blog/2016/02/geogebra-exam-app/

We are currently working with exam boards in several countries developing special versions of our GeoGebra Exam Apps adapted to various needs. For example, the recently added NDerivative command and the Extremum / Roots Tools were added as part of this work. Today, we are releasing several new variants of our GeoGebra Exam Apps.

Note: While the GeoGebra Exam Apps for laptops can be customized by the user, the GeoGebra Exam Apps for Tablets each provide a different preselected set of features.

GeoGebra Exam Apps for Android Tablets

We are committed to making our exam apps available on all platforms, so iPad versions will follow in the coming months. For high-stakes exams, you can also combine the following Android exam apps with additional device-lockdown methods. For low-stakes exams, our exam apps provide a simple way to use students’ own tablets in exams without the need for any special device setup. Please see our GeoGebra Exam Tutorial on how they work.

GeoGebra Exam Simple Calculator

This is “just” a simple calculator, providing a basic version of GeoGebra’s Algebra View, while all other Views are deactivated. There are no GeoGebra tools available and access to commands is restricted to the level of a pocket calculator. However, the GeoGebra Exam Simple Calculator uses the same interface and keyboard that your students are used to using with our other GeoGebra Math Apps.

Play Store link: play.google.com/store/apps/details?id=org.geogebra.examSimpleCalc

GeoGebra Exam Graphing Calculator

The GeoGebra Exam Graphing Calculator combines the Algebra View and 2D Graphics View, while the CAS and 3D Graphics View are deactivated. Additionally, all commands specific to CAS are deactivated as well.

Play Store link: play.google.com/store/apps/details?id=org.geogebra.examGraph

GeoGebra Exam CAS

The GeoGebra Exam CAS provides access to all GeoGebra Views except the 3D Graphics View. There is no restriction concerning the use of commands or tools.

Play Store link: play.google.com/store/apps/details?id=org.geogebra.examCas

GeoGebra Exam Apps for Laptops

GeoGebra Exam for Chromebooks

The GeoGebra Exam App can be customized by the users, allowing them to decide whether they want the CAS and/or 3D Views to be available during the exam.

Chrome Store link: https://chrome.google.com/webstore/detail/geogebra-exam/

GeoGebra Exam Web App

The GeoGebra Exam Web App can be customized by the users, allowing them to decide whether they want the CAS and/or 3D Views to be available during the exam. The app runs in all modern browsers (eg Chrome, Firefox, Internet Explorer 11, Safari) simply by opening www.geogebra.org/exam

Your wish list!

Please try our GeoGebra Exam apps and let us know what you think. Wishes for further improvement or special adaptation to the requirements of your country/state are also very welcome. Just ask! support@geogebra.org

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GeoGebra 3D Grapher Released

We’re pleased to announce that we have now released our new 3D Grapher App for Android. As you can see, it has all the features that you expect from our desktop version’s 3D View such as:

  • Surfaces
  • Geometric objects (spheres, cones, cylinders etc)
  • Quadrics (paraboloids etc)
  • Nets (now draggable to open & close)

Net of a cube (partially folded)Cone and plane cutting the cone horizontallyHyperboloid as ruled surface by Steve Phelps

and as it is a 100% native app, it is super fast & smooth. It also works together with the 2D Graphing Calculator App if you want to work with 2D and 3D simultaneously. We’ve already made lots of improvements from the feedback we’ve received from the 30,000+ users who tried the beta version so many thanks to them!

As always, let us know what you think in the GeoGebra Forum or send us an email to support@geogebra.org and tell us what you would like added and improved over the coming months!

Get the GeoGebra 3D Grapher now from the Play Store

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GeoGebra Global Gathering 2017 – Save the Date!

The pre-registration for our 2017 GeoGebra Global Gathering in Linz, Austria, is now open. 45 countries were represented at the 2015 Global Gathering.

Meet the team. See old friends. Meet new people from around the world. Space is limited, so pre-register early to save the date and your place. See you there!

gathering2017

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GeoGebra 3D Grapher Coming Soon

We’re super-excited to announce that we are just putting the finishing touches to our new 3D Grapher App:

Cross-section of a cube (equilateral triangle)

Cross-section of a cube

Ruled Surface (hyperboloid of one sheet)

Ruled Surface

graph of f(x,y) = sin(x) sin(y)

f(x,y) = sin(x) sin(y)

Please try the beta-test version on your phones and tablets and let us know if you encounter any problems. Then we can release it soon for everyone to play with. Get it now from https://play.google.com/apps/testing/org.geogebra.android.g3d

Capture

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Algebra Reboot!

This week we have released 4 major new features in the Algebra View of our online Graphing Calculator:

Input and Output Rows

Similar to what we have done in the CAS View since 2011, the Algebra View now shows Input and Output rows for most objects types so that you can see the calculation and the result:

av1

Exact Fractions

To go with the the Input and Output rows, we have added the ability to do exact fraction calculations (like you are used to on regular hand-held calculators)

frac1

If you want the approximate answer, then you can press the arrow button to toggle between approximate and exact.

frac2

Automatic Preview

Another major enhancement is that when you are typing an expression in the Algebra View, you now get a preview in the Graphics View, and you also get a warning triangle when the input is not (yet) correct

Input Help

If you click on the “?” icon then you get quick access to the help for all the commands:

blog1

As always you can try out the latest and greatest release here: GeoGebra Graphing Calculator

As you may have noticed, we have been rebranding a little recently so GeoGebraTube has been renamed to GeoGebra Materials, and GeoGebra Math Apps now refers to our whole suite of Apps.
We are also working very hard currently on making GeoGebra Graphing Calculator for iPhone so we will share some more news about that soon (it will look very similar to the Android version which is now at well over 500,000 installs).

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Volume of Spheres with GeoGebra

In the post “Volume of Pyramids with GeoGebra” some elementary proofs of the formula for the volume of a pyramid illustrated with GeoGebra are introduced. In this post, some methods of deriving the formula for the volume of spheres would be presented with the use of GeoGebra.

Eves (1990) presents a proof of the formula as follows. In the figure,
Screenshot_4(Click the figure for the GeoGebra applet)
the area of the cross-section of the hemisphere
Screenshot_5
 the area of the cross-section of the solid at the RHS
Screenshot_6
Hence the areas of the cross-sections of the two solids at the same height are always equal. By Cavalieri’s principle the volumes of two solids are equal. Hence the volume of the sphere
Screenshot_7

Ancient Chinese mathematicians approached the problem in a different way. In the classic problem book the Nine Chapters on the Mathematical Art, the volume of a sphere was incorrectly given as π²d³/16 (d = diameter). Chinese mathematician LIU Hui (劉徽, fl. 3rd century) explained the error as follows. It is known that the ratio of the area of a circle inscribed in a square to the area of the square is π/4. So the ratio of the volume of a cylinder inscribed in a cube to the volume of the cube is also π/4, because each cross-section is a circle inscribed in the square and the ratio of their areas is always π/4.
Screenshot_9Screenshot_10Screenshot_11
(Click the figure for the GeoGebra applet.)

Now consider also the sphere inscribed in the cube. If we assume, incorrectly, that the ratio of the volume of the sphere to the volume of the cylinder is also π/4, then we would get the volume of the sphere is π²d³/16.

LIU Hui pointed out that the object whose volume is 4/π times that of the sphere should be obtained by replacing each of its cross-section by the circumscribing square (see the figure). He called this object a “double box-lid” (Mouhefanggai 蓋合方蓋). He also pointed out that this object is the intersection of two orthogonal cylinder of the same radius (see the figure).
圖片1Screenshot_12
Screenshot_13(Click the figure for the GeoGebra applet.)

LIU Hui was unable to find the volume of the double box-lid. The problem was only solved two centuries later by ZU Gengzhi (祖暅之), the son of the famous mathematician ZU Chongzhi (祖沖之). As shown in the figure below, ZU Gengzhi showed that the volume of the difference between an octant of the double box-lid and the cube containing it is equal to the volume of a pyramid whose volume is one-third of that of the cube. Hence the volume of the double box-lid, and also the volume of the sphere, were found.
Screenshot_18
Screenshot_19(Click the figure for the GeoGebra applet.)

If we try to look at the area of the cross-section of the octant of the double box-lid directly, we could show that its volume is two-third of that of the cube, as shown in the following figures.
Screenshot_20Screenshot_21
Screenshot_23         
Screenshot_22(Click the figure for the GeoGebra applet.)

Final Remark

It is hoped that the GeoGebra applets presented in these two posts on volumes of pyramids and spheres could help teachers to bridge the “logical gaps” (Tzanakis and Arcavi 2000 p.204-207) in the introduction of these formulas to lower form students without proofs. These materials are also valuable to provide problems to motivate and engage students in the teaching and learning of the formulas.

References

Eves, H. 1990. An introduction to the history of mathematics (Sixth Ed.). Saunders College Publishing

Tzanakis, C., Arcavi, A. 2000. ‘Integrating history of mathematics in the classroom: an analytic survey’, in J. Fauvel and J. van Maanen (eds.), History in Mathematics Education, Kluwer Academic Publishers, 201 – 240

Wagner, D . B. (1978) ‘Liu Hui and Tsu Keng-chih on the volume of a sphere’, Chinese Science Vol.3, 59-79

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Followers Feature on GeoGebra Profile Pages

We are pleased to announce another great feature on your GeoGebra profile page! You can now ‘Follow’ your favorite people in the GeoGebra community and get updates whenever they publish new materials.

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The new tab ‘Following’ lists all your Followers, as well as all people you are following, giving you easy access to their profile pages and public materials. As soon as other users start following you, you will receive a cool ‘Followers badge’ on your profile page as well, counting the number of your Followers.

badge_follower_005@2x

Please help us to spread the news, simply by signing in to your GeoGebra account and going to tab ‘Following‘ on your profile page. There, you may search for other users you think create great materials in the GeoGebra community and ‘Follow’ them to keep up-to-date with their newest contributions!

More new features coming soon! Share your ideas and feedback on our Help page.

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GeoGebra Exam App

The new GeoGebra Exam App 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 App …

  • can be easily accessed via www.geogebra.org/exam
  • 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 App 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 support@geogebra.org, thanks!

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