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.
Sine of the Times Blog
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.
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 Pythagoras, scaled...
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. Her textbook, Conceptual and...
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 of the...
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 left with 5...