# Special Quadrilaterals and Their Diagonals

Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?

# The Origami-Math Connection

This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.

# Hats Off to This Aperiodic Tiling

This post examines the role of social media in promoting the discovery of an aperiodic monotile.

# Transformation Dances

This post presents virtual dances based on geometric transformations. As a penguin travels around a polygon, you, as a frog, must match its movements, but with the added challenge of dancing as a reflection, rotation, or dilation of the penguin’s path.

# Transformation Games

This post presents an abundance of games that find their inspiration in three geometric transformations: reflection, rotation, and dilation.

# Generalizing the Pythagorean Theorem

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 ››

# 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:

1. 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.

# 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 SketchpadContinue Reading ››