This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.

# Category Archives: Math Software

# 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.

# 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 ››

# 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 ››*