In geometry, we learn that if we erect squares on the legs of a right triangle, the sum of their areas is equal to the area of the square on the triangle's hypotenuse. This is visual way to conceptualize the Pythagorean Theorem. But now consider the image below that shows a bust of … Continue Reading ››

# Category Archives: Geometry

# A Bevy of Rhombus Constructions

In my January 2020 blog post, I presented a collection of Web Sketchpad construction challenges where the goal was to use each handpicked set of tools to build a rhombus. Could you, for example, construct a rhombus with just a Compass and Parallel tool? How about starting with merely the Reflect … Continue Reading ››

# Euclid Walks the Plank

Using Web Sketchpad, students construct a boardwalk path of equal-length planks to explore the key concepts behind Euclid’s Proposition 1.

# Exploring Scaled Polygons

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.
- Draw rays from the … Continue Reading ››

# Injecting Surprise Into the Triangle Midline Theorem

Pi Day 2022 is now over, but I'm still thinking about a tweet from 10-K Diver: Take two random numbers *X* and *Y* between 0 and 1. What is the probability that the integer nearest to *X*/*Y* is even? The answer—spoiler ahead—is (5 – π)/4. (You can run my Web Sketchpad … Continue Reading ››

# A Paper Folding Investigation from Connected Geometry

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 ››

# Connected Geometry

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 ››*

*Symmetry Challenges*

*In his online 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 ››

*The Swimming Pool Problem*

*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 ››*

*Introducing Web Sketchpad at the 2021 NCTM Annual Meeting*

*NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren't able to attend the conference, you can still take … Continue Reading ››*