Category Archives: Geometry

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 dragging any 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 ››