# Isosceles Triangle Puzzles

As readers of this blog can probably tell, I like puzzles. I especially enjoy taking ordinary mathematical topics that might not seem puzzle worthy and finding ways to inject some challenge, excitement, and mystery into them. This week, I set my sights on isosceles triangles. It's common to encounter isosceles triangles as supporting players in geometric proofs, but … Continue Reading ››

# The Dynamic Ebbinghaus Illusion

We've all seen amazing examples of illusions, but did you know that there is a fertile community of researchers creating new ones? The Best Illusion of the Year contest and website provide a showcase for celebrating illusions. This year's winner for best illusion was created by Christopher D. Blair, Gideon P. … Continue Reading ››

# A Pythagorean Dissection

Nathan Dummitt teaches mathematics and statistics at Columbia Preparatory School in New York, NY. He teaches all four years and is interested in sharing low-threshold, high-ceiling activities with his students. — Guest post by Nathan Dummitt I teach Geometry at a high school in New York City, and I like to start the school year … Continue Reading ››

# The Brouwer Fixed Point Theorem

According to Wikipedia, the Brouwer Fixed Point Theorem, named after mathematician and philosopher Luitzen Brouwer, states that "for any continuous function f mapping a compact convex set into itself, there is a point x0 such that f(x0) = x0. This is a deep theorem,  but one aspect of it is lovely, surprising, and entirely approachable by high-school geometry … Continue Reading ››

# Soccer Challenges: Angling for a Shot on Goal

With the World Cup in our hemisphere, and the US squad having started out with a win over Ghana, my thoughts turned to the mathematics of soccer. My friend Henri Picciotto has a nice page about the shooting angle, the angle within which a shot is on goal, so I thought of using … Continue Reading ››

# Questioning Some Dynamic Geometry Angle Wisdom

For the past eight months, my colleague Scott Steketee and I have collaborated with the authors of the elementary curriculum Everyday Mathematics to design interactive Web Sketchpad models for their next edition. When it came time to create a Sketchpad representation of an isosceles triangle, I built the interactive triangle model below. Try … Continue Reading ››

# Arthur Ganson and the Excitement of Construction

I first encountered the kinetic sculptures of Arthur Ganson nearly 20 years ago at the MIT Museum. Ganson is an engineer, artist, and inventor whose machines, when set in motion, display a grace you would not expect from metal, gears, and other industrial objects. Below is a video of one of … Continue Reading ››

# Playing with Triangular Decompositions

Guest blogger Juan Camilo Acevedo is part of the University of Chicago's Center for Elementary Mathematics and Science Education (CEMSE) digital team, where he develops Sketchpad-based activities for Everyday Mathematics. Currently, he teaches undergraduate language classes at the University of Chicago and is writing his doctoral dissertation on Digital Humanities. Juan holds a BA in … Continue Reading ››

# π Day 2014

π Day has always been a special day for me, from my earliest days. In fact, I've never figured out whether I was so eager to celebrate my first π Day that I jumped the gun and sent my mom into labor early, or whether I just wanted be sure to experience all 24 hours … Continue Reading ››

# A Hidden Polygons Puzzle

Take a look at the two groups of shapes below. Both groups contain an equilateral triangle and a square. Now imagine that you showed students each group and asked them to identify the shapes. Do you think students would do equally well in naming the shapes in group A and group B? Continue Reading ››