GeoGebra apps table

There are many different versions of GeoGebra. I made a table that shows which apps work in different operating systems. Our Lead Developer Mike B. checked and corrected the table. Thanks Mike.

I will try to update this maybe monthly. Link to Google sheets table.

[edit 18.3. Zoltán added Rasperry Pi, thanks.]


Nordic/Baltic GeoGebra Conference photos

10th Nordic&Baltic GeoGebra Conference will be this year in Tarto. Here are my photos from earlier conferences/seminars. I write the first thing I remember about the happenings.

First conference in Reykjavik 10.-11.8.10. Hannu Korhonen had his 65th birthday. photos , conference photos. I lost the original link to published photos, don’t know where the photos are. Published all from my backup, there are duplicates.

7.-10.4. 11 Nordic GeoGebra meeting in Norway. I remember the picnic in the rain, grilling shrimps. photos

2nd Conference. September 30th – October 2nd 2011, Vilnius. I remember Frank Zappa statue and meeting first time Michael. photos

Nggc seminar 2012 Marstrand. Here I learnt about Lasse-Maja. It was cold. photos

3rd Conference in Tartu. I had a birthday party. friday photos, saturday photos, sunday photos

Nordic GeoGebra Seminar january 2013 in copenhagen. We worked hard for the new application. First time I wrote Google Docs with several people at the same time. photos

4th Conference in Copenhagen. I was in the USA, so no photos from me.

014-03-22 GeoGebra Screencast seminar. Bathing in hot water, it was cold out there. Bea told a tale about a troll. photos , more photos

5th Conference. Ylöjärvi. Lots of work for me. photos , Alatskivi photos

2015-03-27 Baltic/Nordic GeoGebra teachers visiting Tartu Erakool. I bought nice shoes. I still have them. photos

6th NBGG -conference in Karlstad. I met teachers from Greenland. photos

May GeoGebra seminar Riga. We filmed movies. GeoGebra Cookbook. photos

7th Conference Trondheim. I learnt to know Markus. Lost in the city. friday photos, saturday photos, sunday photos

Linz IGI 2017. Nice hike on the mountains. photos Not NGGN conference.

8th Nordic/Baltic GeoGebra Conference, Reykjavik 2017. I had one day adventure driving and hiking after the conference. photos, Snæfellsnes

Nordic GeoGebra visitors at Hyl, 2018. Hotel was quite nice, thanks Kari. photos. Sirje added some photos, thanks.

9th Copenhagen. Broke my knee. no photos.

Stockholm, Nordic GeoGebra meeting. Långholmen prison hotel. photos.

Galilei’s beautiful inclined plane theorem

[This a short version of the earlier Finnish blog post, read the original if you want to understand more, of course learn Finnish first.]

I just finished the Galilei biography (Heilbron J.L. Oxford, 2010). A really nice book, it took about half year to read it. Reading it reminded me about the theorems on inclined planes. I have been studying a long time Galilei’s Dialogues books in English. Still most of the geometric proofs are very hard to understand because my intelligence on Euclidian geometry is not very good. In his Discorsi e Dimostrazioni Matematiche, intorno a due nuoue scienze he states in Third Day Theorem VI, Proposition VIIf from the highest or lowest point in a vertical circle there be drawn any inclined planes meeting the circumference the times of descent along these chords are each equal to the other.


If you are familiar with Newtonian mechanics, it is not very hard to prove this :o)

Earlier in the same Third Day in his book he had already shown that the space travelled on constant acceleration is proportional to acceleration and time squared s = ½ a t2. And the acceleration on inclined planes without friction in constant.

We actually have two theorems.

  1. Start from the the top of the circle with particles sliding without friction with different angles. At the same time they should be on the same circle.
  2. Start from the circumference of the circle so that the planes meet at the lowest point, they should meet at the same time.
    But wait a minute, what happens after that. That was the thing that I was wondering when I started this study.

Lets study this with GeoGebra.

1st case

Everybody who loves physics can see that the acceleration on inclined plane without friction is a = g sin alpha , where g is the gravitational acceleration and  alpha the horizontal angle. I will forget g and ½ in acceleration because Galilei’s theorem works on the moons of Jupiter also.
[Just noticed that my alpha was changed to a in WordPress, so after this a in the angle.]

In this 1st case it easier to use polar co-ordinates. In GeoGebra you can create a point in polar co-ordinates, if you use ; as a separator. If you want to create a point from origin with length 2 and angle 20°, the write to Input

XXX = (2; 20°)

You should see the point in Graphics window. This was just a test, so delete XXX or just ignore it.

For us the co-ordinates will be (sin(a°) t²; (-a)°). Think why the other has the negative sign.

Let’s create slider for time t. Write to the Input


Toggle button t and click it with mouse right button and choose object properties Min:0, Max: 5, Increment: 0.1

Write to the Input:

Sequence((sin(a°) t²; (-a)°), a, 0, 180, 10)

If you move the slider t, you will see that the points seem to move on the same circle.


Beautiful. Prove it.

See it on GeoGebra Materials.

Wait for the next story, it even more beautiful.

I am going fishing.

The Finnish Computerized Matriculation Exam System

Matriculation Exam

Before the Finnish high school (upper secondary school) students matriculate (get their high school diploma) they will take part to the Matriculation Exam. They have to pass the exam at least in four subjects. This exam is the only official national test in their 12 year education. So it is really a high stakes test for them. Starting from autumn 2016 the students will use computers in their Matriculation Exam.


The Matriculation Examination Board

A pdf from the Examination Board

Timetable for the Computerized Matriculation Exam in Finland

autumn 2016 German language, geography, philosophy
spring 2017 French, Social studies, psychology
autumn 2017 2nd language Swedish/Finnish, religion, ethics, Health education, History
spring 2018 English, Spanish, Italian, Portuguese, Latin, Biology
autumn 2018 Finnish (Swedish, Sami), Russian, Physics, Chemistry,
spring 2019 Mathematics


Digabi is  the project to create the computerized matriculation exam. Digabi will produce the computer programs and organize the digitalization. Digabi is part of the Examination Board.

In the spring 2015 Digabi published Abitti. It is a system that will let teachers to make tests for their courses with computers. Abitti is the first version of the final digitalized exam.

In October 2015 Abitti was used in the first field test for all Finnish high schools (upper secondary schools). Over 6000 students took part to the test. The test worked very well.

How it will work

The system is based on Linux based Digabi OS operating system. The teacher creates the exam at a web server (run by Digabi) the answers will be evaluated at the same place too. The teacher downloads and installs Abitti server and the student’s client version to  USB memory sticks. Before the test the teacher boots his/her computer (server) with the USB and the students start their computers with the client USB. The student computer finds the server via ethernet/WiFi and students can answer the test questions. The teacher will get the answers to a USB stick and assess the exam.



In the real matriculation examination the teacher server is connected to the Examination Board servers through Internet. WiFi is allowed between school’s server and the students but it will be very hard for the schools to be able to create a secure WiFi system for their exams. So there will be lots of Ethernet cables on the examination rooms. The Abitti system seems to be very secure. If the student tries to hack the system or his/her computer crashes, the system will inform teacher at the server that something has happened.

What is included in the Digabi OS

The exam will use web browser (Iceweasel) to interact with the students. There will be many programs included for the pupils. Right now (autumn 2015) the program list is:

  • LibreOffice
  • GIMP
  • Pinta
  • InkScape
  • Dia
  • wxMaxima
  • Texas Instruments TI-Nspire CAS
  • Casio ClassPad Manager
  • GeoGebra
  • LoggerPro

All programs are not yet in the Digabi OS, because some non open-source programs need licensing, so it is possible the list will change.

In autumn 2015 field test (Finnish language) included text and video material. Students wrote their essays to a form in a browser. In the future there will be many ways to produce the answer. It will be interesting to see how the mathematical equations will be written to the answer sheets.


The Pythagorean MRZKM Theorem


As I was preparing the material for the Chennai GeoGebra Workshop I decided that I will show the theorem that I learnt at the 1st Nordic GeoGebra Conference in Iceland.


The green areas in the Pythagorean Theorem figure are all equal.

I started playing with the figure with GeoGebra and I noticed something funny.


The areas of the red triangle and the blue triangle are equal.

I was really excited and on my workshop I showed it to 25 Indian math teachers. None of them had known about this truth before.

I published my finding in a Finnish Math Facebook group and very soon Kalle Leppälä informed me that the triangle where you draw the squares does not have to be right angle. He also explained the way to prove the theorem.


The red and green areas are equal.

Matti Kalevi Sinisalo found that the result will work on any polygon. (Of course I have not tested it with all the polygons.) So if we start with a pentagon ABCDE and draw the squares with side lengths AB, BC, … DE and draw the quadrangles GIKMO and FHJLN. We will find that the areas are the same.


The red and blue areas are equal.

The Pythagorean MRZKM Theorem


M comes from Mikko, that is me. R is my good friend Revathy Parameswaran who invited me to Chennai GeoGebra Workshop, Z is Zekeriya Karadag who told me to use more geometry in my workshop, K and M come from Facebook group Kalle Leppälä and Matti Kalevi Sinisalo.

The files can be found at GeoGebraTube.

5.8.2015 [The blog database broke down in the beginning of August. I had to recreate the post]
23.10.2015 [some editing and adding Z to the name]

22.10.17 [pictures broke, will fix them some time]

25.2.18 [fixed all the picures]


The Chennai files in Google Drive



Tuesday photos

Wednesday photos

Thursday photos



DATE TIME Group A Group B
13/07/15 9.00-10.30  Inauguration  Inauguration
10.30-12.30PM Dr.KaradagStart up and introducing basics

  • Starting with the basic of GeoGebra: Introducing menu and tools
  • How to use dynamic features: Sliders and Free Objects
  • Introducing function and inverse function
  • Creating linear, quadratic, and sqrt functions
  • Decorating objects
  • Dynamic texts and dynamic colors
Mr. Mikko
1.30-2.30pm Ms.Sangeeta Google apps
2.45 – 4.30pm Dr.KaradagLearning trajectory from geometry to calculus

  • Creating linear functions
  • Calculating the area by using geometric approaches
  • Presenting results by using dynamic texts
  • Creating parabola
  • Using calculus to calculate area
  • Introducing upper sum, lower sum, and Riemann approach
Mr. Mikko
14/0715 9.00-11.00am Dr.KaradagAlgebra and calculus

  • Exploring linear function
    • y=mx
    • y=2x+1 and y=mx+n
  • Exploring parabola
  • Exploring ellipse and hyperbola
  • Translation of functions
    • y= abs(x),   y=abs(x)+k   y = and y= abs(x+k) with slider only
Mr. Mikko
11.15-12.30 Ms.sangeeta Google apps Ms.sangeeta Google apps
1.30-3.30 Dr.KaradagMathematics and Art

  • Creating basic geometric objects by using tools
  • Creating basic geometric objects through Euclidean Perspective
  • Transformational functions
    • Reflecting objects with tools
    • Translating objects with vectors (tools)
    • Rotating objects with tools
    • Rotating objects with matrices
    • Translating objects with matrices
    • Dilating objects with tools
  • Creating an ornament by using tools (sequence and list)
  • Creating dynamic ornament by using slider
3.45-4.15 Mr.MikkoQuestion and answer session Dr.KaradagQuestion and answer session
4.15  valedectory