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.

# All posts by Daniel Scher

# Transformation Games

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

# Dynagraphs of Linear Functions

This post provides three interactive examples of dynagraphs–a powerful representation of functions that emphasizes the behavior and relationship of a function’s independent and dependent variables.

# 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 ››

# Virtual Cuisenaire Rods

*I was happy to collaborate on this blog post with Dr. Stavroula Patsiomitou, a researcher at the Ministry of Education and Religious Affairs in Greece. Dr. Patsiomitou received her PhD from the University of Ioannina and has written extensively about the field of dynamic geometry environments, including Sketchpad and Web Sketchpad. … Continue Reading ››*

*A Bevy of Rhombus Constructions*

*In how many ways can you use dynamic geometry software to build a rhombus that stays a rhombus when its vertices are dragged? This challenge, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties … 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.*

*A Triple Number Line Model for Visualizing Solutions to Equations*

*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 ››*

*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.*

*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 ››*