The Math Education Blog
Dan Anderson commented on my Pentaflake post to observe that the pentaflake can also be created by a random process, sometimes called the Chaos Game. In this game you start with an arbitrary point and dilate it toward a target point that’s randomly chosen from some set of points that you’ve established. You then dilate...
A couple of days ago I got an email from my long-time friend Geri, who was spending some quality Sketchpad time with her 12-year-old grandson Niels. Geri emailed me for advice because Neils was having some trouble figuring out how to construct a pentaflake. Neither Geri nor Niels had any idea that I’d never even...
We’ve all seen amazing examples of illusions, but did you know that there is a fertile community of researchers creating new ones? The Best Illusion of the Year contest and website provide a showcase for celebrating illusions. This year’s winner for best illusion was created by Christopher D. Blair, Gideon P. Caplovitz, and Ryan E.B. Mruczek from the University of Nevada,...
In the early 1990s, Danny Vizcaino, a high school student at Monte Vista High School in California, wrote to Key Curriculum Press noting that Sketchpad did not come with a tool to draw an oval. Undaunted by this omission, Danny had built his own oval with the software and shared it with Key’s editors. As shown in the...
With the World Cup in our hemisphere, and the US squad having started out with a win over Ghana, my thoughts turned to the mathematics of soccer. My friend Henri Picciotto has a nice page about the shooting angle, the angle within which a shot is on goal, so I thought of using Sketchpad to...
Did you know that The Geometer’s Sketchpad is a great tool for creating funhouse mirror pictures? Sure, Sketchpad can reflect, rotate, translate, or dilate a picture, but these operations are rather tame: They transform images uniformly, producing pictures that are easily recognizable versions of the original. By contrast, Sketchpad’s “custom transform” feature allows you to apply non-linear transformations to pictures, resulting in images that...
I first encountered the kinetic sculptures of Arthur Ganson nearly 20 years ago at the MIT Museum. Ganson is an engineer, artist, and inventor whose machines, when set in motion, display a grace you would not expect from metal, gears, and other industrial objects. Below is a video of one of my favorite Ganson sculptures called...
This will be the first in an occasional series of posts that offer interactive Web Sketchpad models for drawing conic sections. My interest in conic sections dates back to the mid 1990s, when I authored Exploring Conic Sections with The Geometer’s Sketchpad for Key Curriculum Press . You can read more about it in my prior...
A little over a year ago, the Museum of Mathematics opened in the heart of New York City. One of my favorite exhibits at the museum is the Human Tree. When you stand in front of the Human Tree screen and wave, your arms are replaced by images of your body. This structure repeats, with more...
A few days ago I led a webinar on the Common Core and Sketchpad for Sketchpad beginners, and I showed four Sketchpad activities aligned with both the Content Standards and the Standards for Mathematical Practice. I mixed it up a bit by showing two activities in which students manipulate prepared sketches, and two activities in...