A new version of Geogebra has been released, in beta. It’s called Geogebra 5.0, and you can see the news about it here. Or, here’s a direct link to launch it right away. Thanks to The Cheap Researcher for the lead on this. As readers of this blog may already know, I love Geogebra!

One of the main highlights is that Geogebra now supports 3D manipulations. Awesome! However, don’t get too excited–it doesn’t let you graph anything except planes. No surfaces. It will do geometric constructions, like spheres and prisms. Using parametric equations and the locus feature, you can coax it into rendering spirals or other space curves. [edit: I figured this was possible, but it actually wasn’t. Not sure why.]

Another highlight, which I find even more exciting, is that Geogebra now has a built in CAS. Here’s a screen shot of me playing around with a few of its features. It also has a ways to go, especially for those who are used to more robust systems like Mathematica/Maple/Derive/TI-89. But this is a great step in the right direction, and 10 points for the open-source camp!

Notice that it can work with polynomials in ways you would expect, it can symbolically integrate and derive (simple things), perform partial fraction decomposition, evaluate limits, and find roots. Here are a few more things it can do. Strangely, it had problems finding the complex roots of a quadratic (easy), but not a cubic (hard). Just take a look at my screen shot. Seeing that it did okay finding the complex roots, I wondered if it could also plot them for me. I started by entering (copying and pasting) the complex zeros as points in Geogebra, which worked. But then I discovered the new ComplexRoot[] function which approximates the roots and plots them on the coordinate plane all at once. Cool! Here’s the screenshot:

The seven complex roots of f(z)=z^7+5z^4-z^2+z-15

As you can see, I asked for the roots of a 7th degree polynomial. Since the polynomial had real coefficients, notice that every zero’s conjugate is also a zero, as we’d expect. And we also expect that at least one solution of an odd-degreed polynomial will be real (notice this one has only one real root, approximately 1.22).

That’s all I’ve discovered so far. I’ll let you know if I come across anything else exciting. Keep in mind that this is beta, so the final release will likely have all the bugs worked out and more features.