Maths in a nutshell
Wolfram Research's Mathematica celebrated it's 20th birthday last week. I haven't used it in a while, but it was a very nice tool to do mechanical simulations. I'm glad to learn that they now have a free viewer which plays thousands of free demonstrations and notebooks on many areas like: architecture, fractals, 3D Graphics, art, patterns, chaos, mechanics, and more.
Mathematica Player is an innovative new take on viewer applications. Rather than just a reader, like Acrobat Reader, or a thin runtime, like Flash Player, Mathematica Player has the full Mathematica engine embedded right there --ready to make documents come alive or to power applets. (Of course, don't forget it can read notebooks too!) Because Player-interactive documents are so easy to make using Mathematica 6 technology, thousands of these are already freely available at The Wolfram Demonstrations Project--with more supplied each day by researchers, educators, students, and professionals. Yet there's one aspect that's just like other players: it's free. Download it now.
If you need an "oranges and apples" approach... here's a bit nutty way of exercising pattern sequences. (via: Not Quite Perfect) It might look... well, oranges and apples... but it's actually a squirrel! Seriously, I had to scratch my head several times with some sequences... actually not with the sequence itself, but trying to figure out the formula. Usually we just discover the pattern intuitively, we never actually think about the mathematical formula behind that. For example, a sequence as simple as: 5, 4, 3, 2... you may know that the next number is 1, and then 0, etc... but what about the 20th number in the sequence? You may need to think of a formula to calculate that ( 6-n=x ). After shaking some rust out of my brain, I managed to get 1404 points... I have no idea if that's good or bad, but it left me with a headache.