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:

Orthocenter of a Triangle

Angle-Side-Angle Triangle Congruence

Compound Curve and System of Inequalities

Corresponding Angles formed by a Transversal

The Fibonacci Sequence

The Four-Color Theorem

Linear Inequality Solution on a Number Line

Medians, Circumcenter, and Tangents

A Catalog of Angles: Acute, Right, Obtuse, and Straight

The Pythagorean Theorem

Centroid of a Triangle

Incenter of a Triangle

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Strange Attractors

This post isn’t about the strange attractors you hear of in chaos theory; rather, it’s about an excellent poetry anthology edited by Sarah Glaz and Joanne Growney. I’ve linked to Joanne’s blog, Intersections, before. After showing it to my school’s librarian, she ordered a copy of Strange Attractors, and it arrived a few days ago.

I haven’t had chance to really delve into it, but it looks wonderful. Glaz and Growney have selected poems from the beginning of recorded history up to the present. What holds it all together is their subject matter: love. Yes, mathematicians are susceptible to it, and these poems are ample illustration of the many ways math and poetry complement each other in expressing that emotion.

Most of the poets use plain words to get their point across, but there are several clever exceptions. I especially like this one by Kaz Maslanka, entitled “Sacrifice and Bliss”:

 

 

It reminds me of a Tolstoy quote I have in my classroom: “A man is like a fraction whose numerator is what he is, and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.”

Anyway, even if you’ve forgotten most of the math you learned in high school, you’ll find plenty of wonderful poetry to enjoy in this anthology. If you love math, you’ll derive (!) even more pleasure from it. If you teach math, Strange Attractors will be an invaluable resource for you and your students.

A Really Useful Online Graphing Calculator

The good people at Desmos have made an excellent online graphing calculator even better. It’s incredibly fast and versatile. For example, if you input y = m*x + b, it will automatically ask you if you want to create sliders for “m” and “b”. Here’s an example of a quadratic function with sliders:

It will plot implicit relations:

As well as inequalities:

There’s even a “Share” button that lets you post your creation to Facebook, Twitter, or Google+. Once you create an account, you can save your graphs online, to be used later. There are countless applications of this product in the math classroom.

Click here to try it out!

Download a brief User’s Guide here.

Forget Economic Inequalities, Let’s Solve Nonlinear Inequalities!

As the presidential candidates begin their final week of campaigning, let’s take a break from all the rhetoric and enjoy some nice nonlinear inequalities. Linear inequalities are fairly straightforward: solve for x and make sure you switch the direction of the inequality if you multiply or divide by a negative term. Nonlinear inequalities are trickier: you need to completely factor the expression, so you can build a sign chart on the number line. Confused? Don’t worry; everything is made clear in the screencast below: