Does it exist a free interactive geometry software, like GeoGebra, which works for 3D geometry? I would be able to draw spheres, great circles, and so on.
3D software like GeoGebra
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I think you can, to a limited extent, use Google Sketchup, but that's not really the same.
Cabri3D is probably the most like what you want, but it's commercial. Autograph, also commercial, may do some of that kind of stuff, but I'm not sure.
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Geomview is fairly flexible, and allows you to work in Euclidean, spherical or hyperbolic geometry. Depending on which operating system you use it might be easier or harder to get it installed. It made it into the Ubuntu repositories recently, so if you're running Ubuntu it takes little effort to install.
That said, it's not the easiest software to use -- quite a ways away from the interface of GeoGebra. More often than not, if I need a high-quality rendered image of something 3-dimensional, I code a PovRay script and render it.
Blender is open-source and interactive. It appears to be quite flexible -- it's used to produce models for 3d video games, for example. I haven't really got comfortable using it, though.
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Try kd3-surf if you haven't yet found it at http://k3dsurf.sourceforge.net/
Free software and small file size, easy to manipulate.
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If you're on a mac, theres a plotting software build in.
Go to Applications / Utilities / Grapher.
It's easy and powerful, can plot 2D and 3D graphs.
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FEOGWEBRA 3D IS TOP NOCH, BUT HERE ARE SOME ALTERNATVES:
Archimedes Geo3Dhttp://archimedesgeo3d.weebly.com/
THE CLASSIC CABRI 3D: https://cabri.com/en/enterprise/cabri-3d/index.html CALQUES 3D> http://www.calques3d.org/( YHE ONLY ONE THAT OFFERS 3D LOCI
You can try pgftikz http://www.texample.net/tikz/examples/