Dynamic spatial geometry
The dynamic spatial geometry is a relatively young branch of dynamic geometry . As in the two-dimensional case, it is understood to mean the interactive creation of geometric constructions on the computer . The concept of geometric construction is here generalized to space in an obvious way. Constructions with compass and level ruler are added to the constructions with compass and ruler . "Dynamic" in this context means that base points can be moved freely (see pull mode ).
While synthetic geometry in the plane has a millennia-old tradition, synthetic geometry in space has hardly been used so far. In the curricula of general schools, too, spatial geometry takes place almost exclusively in the context of analytical geometry . Investigations as to whether a synthetic approach, for example , would train the spatial conception better than the usual, rather abstract, analytical way are still pending. This is one of the reasons why, in contrast to the situation with dynamic geometry programs for constructions in the plane, there are so far only a few programs that implement the concept of dynamic spatial geometry .
software
In 2003 the spatial geometry software "Descartes3D" was published, which was specially produced for high school and university mathematics. With the support of 3D glasses, the presentations really appear three-dimensional in front of the screen if required. Descartes is not a dynamic spatial geometry program in the true sense of the word because of the lack of a train mode and the lack of local lines / surfaces.
In 2004 the company Cabrilog, which can already be considered a pioneer of dynamic geometry in the two-dimensional, published its dynamic spatial geometry software "Cabri3D". The programs "Archimedes Geo3D" and "Vektoris3D", which appeared in 2006, offer similar properties, but each set different priorities in detail. While the selection of basic objects is smaller than with Descartes3D and Cabri3D (e.g. cylinders and cones as well as the Platonic solids are missing ), it allows you to add your own commands via macros . Furthermore, Archimedes extends the concept of the locus, known from two-dimensional dynamic geometry programs, to locus lines and planes in space. Finally, it has flexible term input. The navigation in the drawing is based more on common 3D games than with Descartes3D or Cabri3D and allows you to zoom in continuously.
Kapieren.de and Ernst Klett Verlag have been using the Vektoris3D software since 2006, which pursues a curriculum-oriented approach with a focus on textbook content and presentation. The software has its own scripting language.
Since autumn 2014, version 5.0 of the now widespread dynamic geometry software Geogebra has also had a 3D mode.