GeoGebra, mathematics in motion

GeoGebra is a software dynamic geometry, that is, it allows to make geometric constructions and give them life (read «animate them») in order to achieve this not only to reach an optimal understanding of the geometry but also complex operations and simulations either from other areas of the Mathematics or other disciplines such as Physics or the Economy.

Sometimes they ask me why I decided to study Mathematics and the panorama becomes recurrent. I try to explain what for me are simple and forceful reasons: how can I not love Mathematics if in it you can appreciate a magnificent beauty - modest but sublime - if it is the owner of truth and teacher of rigor and order, if it teaches think, communicate and be creative (…) ?: But after a few minutes in which I try in an almost superhuman way to make my interlocutor understand at least one of my motives, he rushes to change the subject. If the law of averages is true, we are very, very few of us who are passionate about Mathematics to the point of making it our main occupation. Although it is true that it is very difficult for the "modern student" to acquire that special taste for it or in fact to fully understand some part of the enormous thematic spectrum it covers, all is not yet lost. An interesting mathematical software comes from France: GeoGebra to "put the chest" to such a challenge.

GeoGebra is a dynamic geometry program, which means that with it we can generate constructions from points, segments, lines, etc. and animate them to recreate different geometric formulations and thus learn better or better teach the desired concepts. But it doesn't just stop there; it also handles calculus and algebra within the same dynamic environment.

Objects can be entered either with clicks of the pointer in the graphical view or analytically in a simple but very functional console. The number of tools that GeoGebra operates to manipulate objects is impressive to the point that practically nothing has escaped its developers (led by Markus Hohenwarter) to the point that it is not an exaggeration to say that anything imaginable in 2D can be done in GeoGebra .

But GeoGebra goes even further: automated animations and presentations can be created, its constructions can be exported to different useful formats such as PNG, animated GIF, EPS, PDF, PsTricks (Yes, it exports to LaTeX code !!!), among others. ; and even external objects (such as images) can be imported and involved within the mathematical formulation.

Its interface is very simple and pleasant. In it we find a geometric view, an algebraic view and, if desired, a spreadsheet view.

This is GeoGebra playing with some concepts typical of Euclidean geometry (the bisectors of the sides and the circumcenter):

Here with some elements of calculation (the sine function, its derivative, its integral from zero to pi and an approximation by means of Taylor series):

Here doing a Physics simulation (a parabolic concave mirror):

GeoGebra's capabilities can satisfy any audience of any level. If the user so requires, he can even represent - if he is willing to acquire a high level in handling the program - fractals and objects and simulations in 3D (even when it was designed for 2D !!!).

En http://www.geogebratube.org/?lang=es There is a huge database of projects made by many enthusiasts of the program, classified by categories and some of them are really impressive.

The current version of GeoGebra is 4.0.32.0 and by popular demand, for version 5 of the program there will already be a simple but powerful additional environment to do everything imaginable in 3D (the beta is already there and promises a lot).

To get GeoGebra, just look at the package manager of your distro and it is very likely that the program is only one click away. If this is not your case, on the official website of the project http://www.geogebra.org/cms/es you can access the packages and the instructions to add the respective repositories.

I don't want to take more time from you, my friend; so I hope to motivate you to look at Mathematics from now on with different eyes thanks to GeoGebra. If you already like this wonderful area of ​​knowledge, I congratulate you; But if this is not your case, give GeoGebra a chance so that through it you understand how wonderful this discipline is that the great Galileo came to describe as the "language of the Universe".