GeoGebra
GeoGebra ( portmanteau word from geometry and algebra ) is a dynamic geometry software (DGS ), which provides their geometric objects not only the usual geometric and algebraic interface. Geometries can therefore be not only in the drawing is created and changed, but also by the specification or manipulation of equations. In addition to elementary geometric objects to allow for newer versions of GeoGebra also the creation of function graphs, level curves and vectors, and have a built- in computer algebra systems (CAS) and a spreadsheet. Because this functionality is GeoGebra can not be inserted only in geometry, but also in other areas of mathematics such as calculus, linear algebra, or stochastic. Since a change in a window, such as geometry, dynamic effect on the images in the other windows, as algebra Geogebra is also referred to as a dynamic mathematical software. The majority of GeoGebra is free software. The program is now available in 50 languages.
GeoGebra has won several awards, including the European educational software Prize in 2002 and the German educational software price 2004. The software was developed in large part by Markus Hohenwarter for the thesis and his doctoral dissertation at the University of Salzburg since 2001. Meanwhile, GeoGebra is an international product, are involved in the development of different countries.
The program is available for the operating systems Windows, Linux, Mac OS X and since September 2013, for Android. Meanwhile, it is available in version 4.4. GeoGebra requires the Java Runtime Environment ( JRE). The current version and a pre-release version with the latest developments on the homepage via Java Web Start downloaded and used.
Capabilities of the software
GeoGebra can represent both geometric designs on a blank workspace and function graphs in a coordinate system. With the help of any placeable sliders can be easily varied in the so-called pull mode, the size of parameters and the resulting changes they are considered dynamic.
GeoGebra here is different from other interactive geometry programs in that it displays as a single program for all mathematical objects an algebraic definition.
The user can exert influence on the type of representation on various setting options. So, for example, points in Cartesian coordinates, complex number or polar coordinates are given and illustrated.
Since version 3.2, a spreadsheet is included that offers cooperation with the character sheet in addition to the usual capabilities of such a program. So numbers from a drawing and read objects can be dropped from the table.
Since version 4.2 GeoGebra offers not only an algebraic interface to the geometric objects, but a separate console interface also provides access to the internal computer algebra system ( MPReduce ).
Individual features in selection (each representation and calculation)
- Graph of functions depending on parameters
- Definite integrals and antiderivatives
- Curvature function graphs
- Zeros, extrema and inflection points entirely rational functions
- Tangent and normal at function graph
- Taylor polynomials
- Asymptotes of hyperbolas
- Straight line and its slope, half-lines
- Surface of arbitrary polygons and regular polygons
- Length of routes
- Size of angles
- Conic sections: ellipse, circle, Polar
- Sectors of a circle, arcs, radius
- Pictures: axis mirroring, point reflection, parallel translation, rotation, stretching Centric
- Multiplying and factoring polynomials
- Vectors normal vector
- Representation and complex number calculation
- Calculations with matrices
License
GeoGebra is free for non- commercial use. Commercial use of the program is only allowed if royalties are paid. The majority of GeoGebra is under the GNU General Public License as free software. Some parts, such as the installation program, but under licenses which prohibit commercial use, and are therefore not free software.