# 2013 Winterim: Light, Math & Color

I taught another three-week stained-glass mini-course this year. After my students learn the basic technique of copper-foil stained glass windows, they research a math topic, write a paper on it, and illustrate it with a window of their own design. Topics this year included systems of inequalities, the Fibonacci Sequence, corresponding angles formed by two lines and a transversal, the Four-Color Theorem, and the Pythagorean Theorem among others.

Here’s a gallery of their finished windows:

# Invasion of the Parabolas

This screencast (hopefully) covers the basics of parabolas: focus, vertex, directrix, and the standard form of an equation of a parabola. Why do we ask students to spend so much time on these things? Because math teachers are by and large cruel and cynical adults who enjoy inflicting mental anguish on adolescents. Not!

Actually, parabolas are very important because they model so many things in life – not the least of which is projectile motion. The next time you quench your thirst at a water fountain, take a look at the stream of water: yes, that’s a parabola. If you look at a cross section of a satellite dish, you’re looking at a parabola. If you take a flashlight apart, and look at the reflective bowl surrounding the light bulb, that’s a parabola. Parabolic collectors are used to enhance the sensitivity of microphones.

Parabolas are everywhere – fortunately, they are completely harmless.

# Exponential and Logarithmic Equations

Now that we’ve covered the properties of exponential and logarithmic functions, we’re ready to solve equations involving them! Because they are inverse functions, we use one to solve the other.You can learn more by watching the screencast below:

# The Power of Logarithms

Logarithms. The word can strike terror in the hearts of algebra and precalculus students everywhere. However, once you understand their secret, there is nothing to fear. Logarithms are simply powers of numbers. They’re exponents! For example, when you ask yourself, “What power of 3 would give me 81?”, and you answer “4”, you just figured out a logarithm. 4 is the log of 81, base 3.

See? That wasn’t so scary, was it? Now watch my latest screencast to learn more about these misunderstand numbers.