# It’s Time To Think Rationally

This screencast is all about rational functions, where one polynomial divides another. It’s a fairly complicated process to sketch them, given all the asymptotes that show up when the denominator approaches zero. However, if you sit through this slightly longer than usual video, I show off my new toy: FluidMath! I’m planning on writing a post soon that displays more of its features, but I’m still learning the basics of it. I haven’t been this excited and impressed about math-related software since many years ago when I first saw Geometer’s Sketchpad on a Mac Classic.

# Real or Imaginary? Both – It’s Kind Of Complex

For most of us, real numbers are enough to do the job of day-to-day math. However, there is another set of numbers that are outside the real numbers: the unfortunately named imaginary numbers. Unfortunate, because they have real-life applications, such as in electrical engineering. Imaginary numbers are based on the square root of -1. No, you won’t go blind if you take the square root of a negative number, you just get a whole new set of numbers to play with!

Combining the set of real numbers with the set of imaginary numbers, gives us the set of complex numbers. These numbers are graphed in the complex plane, which is where fractals reside!

# Angles and Triangles

I know most people lie awake at night wondering why the sum of the interior angles of a triangle always add up to 180 degrees. Believe it or not, there is a very good reason, and you can see it here. As an added bonus, you also get to see how exterior angles and remote interior angles of triangles are related!

# Life Is Change – Calculus Figures It Out

We’re getting into real calculus with this topic: Basic Differentiation. Scared of calculus? You shouldn’t be. If you understand that a slope is a rate of change (i.e. miles per hour, etc.), then you’re well on the way to understanding calculus. Algebra deals with average rates of change, whereas calculus enables us to figure out instantaneous rates of change, called derivatives.  What’s really amazing is how calculus can find the slope of a curve at a single point! And applying some very simple techniques gives us these derivatives with very little effort. Impossible, you say? Watch below: