Back again in Austria; I’ve been to two additional conferences during the last two weeks. The first one, in Serbia, was about computer aided mathematics education, and the second one was also, but with Czech colleagues from České Budějovice.
Sightseeing in Belgrade with Ivan, Gábor and Simon
In Serbia I took part at many nice talks. Maybe the best one, Alfred Wassermann’s new project Sketchometry was a real joy to see. The beta version already recognizes several gestures from the user, both by mouse on a PC or fingers on a tablet. By clicking the + sign on the bottom right, one can start to try this free product on ones own very quickly. Alfred confessed that the first minute was usually a bad experience for some users, but after then the usage became really intuitive and joyful. Anyway, this is really cool, as Gábor (the lead web developer at GeoGebra) mentioned after the introductory talk.
Sketchometry uses JSXGraph as its underlying DGS, and also Darko Drakulic, a contributor of GeoGebra in developing a numerical method for locus line visualization for Google Summer of Code (GSoC) 2011, wrote a nice frontend for it, and gave a talk about his development at the conference. JSXGraph, Wassermann’s main project in the recent years, seems to be a reliable backend for such lightweight GUIs. This is an important issue for smartphones, and at GeoGebra we also plan to reduce the application size as much as possible.
So, I’m back in Austria now, but the life did not stop here, either. Our fresh GSoC 2012 student, Damien Desfontaines did very good improvements on the area method for the OpenGeoProver subsystem. Now his brand new prover is capable of proving 18 theorems or statements from the 44 test cases. This result is remarkable enough if we consider his age (Damien is 19 years old!), the time he spent with the implementation (not more than 3 weeks), and that his work gives far the fastest computation for Desargues’s theorem (142 milliseconds).
We are happy to announce that our 100th GeoGebra Institute has been established in Asia! It is our new Mongolian GeoGebra Institute led by Navchaa Tserendorj.
We are delighted to see that our community is rapidly expanding all over the world! Please let us know if you are trying to set up a new GeoGebra Institute and would need our help or if you have any contacts for people who are considering establishing new GeoGebra Institutes.
Feel free to ask questions in comment here below the post or send an e-mail to institutes at geogebra org.
GeoGebra in the browser. That is our new goal. And not just that. With the collaboration with Google, we have developed the GeoGebra Chrome App. It is basically GeoGebra in the browser with the extra functionality of storing the ggb files in the cloud using Google Drive.
Visit the Chrome Web Store and search for GeoGebra. Two Apps are there in the Store, one for the GeoGebraTube and the shiny new GeoGebra Web App.
After installing and launching the application, you should allow the app access to your Google Drive:
The app looks almost identical to the Java version:
And it not only looks like the Java version, but works like it too:
As a nice extra, today we’ve added Edit -> Insert Image from -> Webcam. You can then rotate/reflect/etc the image as you can do when you insert an image in the Java version.
You have to enable a flag in Chrome for this to work at the moment, details here:
http://www.geogebra.org/forum/viewtopic.php?f=48&t=27868
What is working:
Bonus features that the Java version doesn’t have:
We hope to soon start work on adding:
ICME offers a good opportunity for the GeoGebra Community to meet colleagues from all around the world. Also, we can involve many colleagues and teachers from Korea and other Asian countries.
Visit the official conference website for more information. There are two weeks left till the registration closes. Look at the poster below and join us if you live nearby or plan to go to the ICME.
Deadlines
Please use the registration form if you plan to be there with us.
All the participants of the conference are going to get the following special limited edition t-shirt:
Are we going to meet in Korea? Please share the information about the conference. Let your colleges, friends know about the GeoGebra conference in Korea. You can use the poster, or just link to this post or directly to the conference website.
Ivan Petrović, PhD student at University of Belgrade
The EACA conference has just ended, but the hard development in theorem proving did not stop. Our Serbian contributor Ivan Petrović did very nice improvements on GeoGebra by working hard on the OpenGeoProver (OGP) prototype during the last week. Now the desktop version of GeoGebra has 5 possible ways to prove a statement, and OGP, the latest one, does a really good job.
Predrag Janičić, associate professor at University of Belgrade
Now the recent benchmarks show that Ivan’s prover (based on Predrag Janičić‘s GCLC, but fully rewritten in Java) gives the correct answer in 40 out of the 44 test cases, and beats the other provers in the most difficult computations, namely the Desargues’s theorem and the Simson line. In general, it has the second best average in computation time (Recio: 89, OGP: 315, Botana: 540, PureSymbolic: 2091 ms), and the best standard deviation (OGP: 250, Recio: 399, Botana: 2226, PureSymbolic: 9467 ms), which means OGP is the most stable prover engine for GeoGebra at the moment. (The 5th prover is the Auto method: it tries to find the best prover engine by using some heuristics. This is the default in GeoGebra.)
The official announcement of our joint work will be on 22 June at the CADGME conference in Novi Sad, Serbia.
Last week I spent two wonderful days in Ireland. Maynooth is a little city not far from Dublin. The 7th Annual Conference in Mathematics and Statistics Service Teaching and Learning had a GeoGebra day. I had the chance to talk about community and development news.
You can see the Prezi used for the talk here:
After the keynote, about 20 teachers attended the workshop. The following topics were discussed:
Thank you GeoGebra Institute of Dublin for organizing this amazing event. And if you visit Maynooth, visit the building called “Logic”, where the maths department resides:
Days are passing and the summer conference time is getting closer and closer. In two weeks we (Simon and I) will attend EACA 2012 in Spain, and then CADGME 2012 in Serbia. For both we are preparing with the new features of GeoGebra, namely the provers.
Even during the last week there were lots of improvements on the user interface. Now GeoGebra accepts statements in a∥b, c⊥d, E≟F (or E==F) format, and both segments and lines can be used in many proofs. The non-degeneracy conditions are also reported for almost all investigations. These are maybe nuances for a researcher, but important details for most users, for example students: GeoGebra must be intuitive in all subtopics of the mathematics. This is what we try to focus on: to ease understanding of difficult things.
This screenshot shows a non-degeneracy condition for the triangle midsegment theorem: if the points A and B are different, then the theorem is true. Here we used the "parallel" sign to define the statement. The URL shows that Google hosts the web version of GeoGebra, but also an offline version can be installed for the Google Chrome browser.
For those who are interested in the very technical information, we updated the wiki page for theorem proving on our developers’ site. The newest results for the benchmarking suite are also available here.
Well, I forgot my own introduction in the first post, but maybe it is more important for me that I work in a great team. Balazs already wrote a few words about himself; I am also a mathematics teacher from Hungary, but currently working in Linz, Austria, personally with Markus and his student team.
Both of my kids are also GeoGebra fans, but they are too young to really understand the difference between proof and verification yet. A proof is a theoretical confirmation that a statement (for example, “the bisector lines of a triangle are concurrent”) is always true. A verification is usually an experiment, that the statement is indeed true, by choosing a large set of examples.
GeoGebra is not the first software which provides proving. The first pieces of software were written back in the 1980’s. But oddly enough, many of the first scientific papers were also written by researchers of University of Linz, lead by Professor Bruno Buchberger, founder of the Gröbner basis theory.
Now GeoGebra has several built-in methods to decide if a statement is true in general or not, and one of the used methods is based on Gröbner bases. To avoid heavy computations on a single workstation, we can outsource them to another software, namely Singular, which runs as a web service remotely. On the other hand, we also use a sophisticated method to avoid symbolic computations completely. Professor Tomas Recio, a Spanish expert of algebraic geometry, developed this idea, and Simon Weitzhofer (mentioned in my first post) implemented it in Java recently.
Luckily enough, even other colleagues joined us from different countries. Professor Francisco Botana, a pioneer in open source based mathematics, also from Spain, and Professor Predrag Janicic from University of Belgrade, lead developer of GCLC, offered their help in extending GeoGebra with state-of-the-art methods to provide fast computations. Also Ivan Petrovic, a PhD student of Predrag, works on the open sourced, Java based OpenGeoProver, to enhance it to be an optional prover engine for GeoGebra. We also have a Google Summer of Code 2012 student, Damien Desfontaines from Paris, France, in our group, who helps Ivan to implement the area method, to extend the set of applicable statements for proving. One day maybe we will have readable proofs as well, since the fast algorithms usually don’t give acceptable output for a human. But currently we are really satisfied with some yes/no/unknown result, which should also be used in both experimenting and teaching mathematics.
The basics are working already good, fast and intuitively enough. See this table for an overview: Botana’s method is the Singular based Gröbner basis calculation, pure symbolic method is just dealing with parametric polynomials in Java internally, the OpenGeoProver backend is not listed yet. (The numbers mean milliseconds.) One can also try Recio’s method (and as fallback, the pure symbolic method) in the web version of GeoGebra, or wait for the desktop version (4.1.81.0 should be stable enough, but it is not released yet at the moment), or just watch this YouTube video. For those who are interested in the details, the documentation of the Prove and ProveDetails commands will also help.
After some hard work with Simon Weitzhofer, an undergraduate student at Johannes Kepler University, Linz, Austria, we finally published a GeoGebraWeb version which contains a built-in computer algebra system (CAS), “binary the same” to the desktop version of GeoGebra.
Ted Kosan, a pioneer of converting computer algebra systems from different languages to others, was one of the first hard worker in this long story. Ted, the lead developer of MathPiper, also did a great effort on converting YaCAS into Java, back in 2008. Because of Reduce has been open sourced since December 2008, and a Java interface (JLisp) was also available for it, Ted decided to try to convert it to JavaScript by using the Google Web Toolkit “Java to JavaScript” compiler (GWT). His adventure was inspired by Gábor Ancsin, a former web designer, who had surprisingly great results in compiling the GeoGebra source code into JavaScript with GWT. Now Ted’s work is a part of Reduce under the name “JSLisp“, and it is also built into GeoGebra as “GGBReduce“. With Ted’s help we have been using the Java version of Reduce by inserting its bytecode stream for the desktop platform, and finally we were also able to put the same bytecode into GeoGebraWeb as a static text. (In fact, Ted was already finished with his prototype back in May 2011.)
To try it out, the user should simply go to the alpha test page of the web platform version of GeoGebra. Then enter
f(x)=x^2*sin(x)
into the input box, press ENTER, and as another command, enter
g(x)=f'(x)
In some seconds (depending on the internet connection and the machine speed, and also the browser) the output g(x)=x^2*cos(x)+2x*sin(x) will be shown in the Algebra View on the left. Google Chrome users may want to try to install GeoGebra from the Google webstore as well to make all of this work offline on their workstation, too.
Yes! No magic any longer – a full featured computer algebra system fits in HTML5 and JavaScript. The next step is to do it faster – to offer convenient use for smartphone users as well. A smartphone can be really slow, and have just limited resources, so this sounds another great challenge.
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