Do You Have The Stomach For A Geometry Puzzle?

I’ve been reading Clifford Pickover’s excellent and entertaining The Math Book. Its topics are arranged chronologically, with each entry just one page long and paired with a beautiful illustration. It’s the perfect book to keep by your easy chair, where you can pick it up and have a quick read.

One of the entries is about Archimedes’ Stomachion, which is pictured below. If you print it and cut out the pieces, there are 17,152 different ways you can arrange them into a square!

I constructed the one below using GeoGebra, but for a geometry class that is learning the classic straightedge and compass constructions, it would be a nice exercise to draw one using those tools. The only constructions necessary are midpoint of a segment and parallel line through a point.

Get out your scissors and have fun!

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

WCYDWT: Geometry in Geography

As I was flying home from the 2012 NAIS Annual Conference in Seattle, I looked out airplane’s window and saw these patterns in the farmland below. I’m going to figure out a way to use them in my geometry classes. We just finished learning about areas of polygons and circles, so I’m sure these pictures can spark some interesting questions and investigations.

By the way, WCYDWT stands for “What Can You Do With This”, a teaching technique pioneered and championed by Dan Meyer. There’s a permanent link to his blog at the bottom of my home page.

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Through a Prism (Darkly)

I’m heading to Seattle this week for the National Association of Independent Schools’ annual conference, so I am preparing screencasts for all the classes I’ll be absent from. This one is for my geometry students – we just wrapped up areas of polygons and circles, so it’s time to add another dimension! Prisms are the simplest solids to work with, so that’s how I introduce surface area and volume. All the dirty details are included in the screencast below: