There is an amazing tool out there for teaching and learning about Math (and the world) and not enough people know about it. If you have never tried it out before, you should head over to Wolfram Alpha right now. Wolfram Alpha describes itself as a computational knowledge engine which may not mean much to people and the sparse home page with just a search box doesn’t help if you have never heard of it before. But as a starter you could think of it as the intersection of the world’s best graphing calculator with all the numerical data from Wikipedia.
For instance, here is a simple query that compares the US population to that of Germany. As you can see Wolfram Alpha not only pulls up the information but also charts it for you! It is also very clever about understanding different formulation for the same query. So instead of “US population; Germany population” you could also ask for “US vs German population” and get the same results. Here is just one other query to show how much data is available at your fingertips and immediately graphed.
One way to use this is to explore mathematical ideas. For instance, a while back I talked about spirals in my first “Math & Beauty” post. Now Wolfram Alpha let’s you beautifully explore this topic. Just start with the very simple query of “spiral” and you will see a number of named spiral curves. You can then drill into any one of them, such as the Archimedian Spiral. Wolfram Alpha shows them to you both graphically and as parametric and polar equations. They also provide many more great examples.
Wolfram Alpha has also been extending their specific educational offerings. For instance they have a series of iOS apps to support studying specific parts of math. They also just released a problem generator to help give you lots of practice. All in all there is so much there – and most of it is either free or cheap!
