In Algebra 1, I was the king of solving for x. Algebraic manipulation was fun and satisfying, and I was good at it. But my confidence was shaken when I encountered a test question of the variety 4x + 5 = 4x – 3. After subtracting 4x from both sides, I was … Continue Reading ››
Below are some common methods that geometry curricula offer for constructing scaled polygons:
- Place a polygon on the coordinate plane, pick the origin as the center of dilation, scale each vertex by some specified amount by using its coordinates, and then connect the scaled vertices.
In a prior post, I shared some good news: The Connected Geometry high-school curriculum authored by Education Development Center (EDC) is now available for free. I could easily devote every future blog post to a tasty Connected Geometry morsel, but I'll restrict myself to just a few. The investigation … Continue Reading ››
It's that time of year when we start seeing "best of" lists for books, movies, music and the like. In that spirit, but stretching way beyond the past year, some of my favorite geometry textbooks include Geometry: Seeing, Doing, Understanding (Harold Jacobs), Discovering Geometry (Michael Serra), and Geometry: A Transformation … Continue Reading ››
In his article Simply Symmetric, Michael de Villiers observes that symmetry is a powerful but often overlooked tool for formulating proofs:
Most primary geometry curricula around the world introduce the concept of line symmetry fairly early, and sometimes also that of rotational, translational and glide reflective symmetry. … Continue Reading ››
In a prior blog post, I presented an uncommon method for solving the well-known Burning Tent problem. My solution, modeled on the approach in the Connected Geometry curriculum, used a dynamic ellipse to pinpoint the optimal solution. Now, I'd like to offer a related problem from Connected Geometry where … Continue Reading ››
In a previous post, I described two different approaches to solving the Burning Tent optimization problem. Now I'd like to offer a related problem that I assigned many years ago to my pre-service mathematics teachers at New York University.
A cowgirl wants to give her horse some food and … Continue Reading ››
How can you identify a lover of math? Casually mention a burning tent and notice if her first thought is how to minimize her path to a river and then to the tent to douse the flames. Here is a full statement of this classic geometry problem:
Ah, the great … Continue Reading ››