Category Archives: Math Software

Pentaflake Chaos

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 … Continue Reading ››
pentflake

How do you make … a pentaflake?

pentflakeA 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 … Continue Reading ››

The Dynamic Ebbinghaus Illusion

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 … Continue Reading ››

The Brouwer Fixed Point Theorem

According to Wikipedia, the Brouwer Fixed Point Theorem, named after mathematician and philosopher Luitzen Brouwer, states that "for any continuous function f mapping a compact convex set into itself, there is a point x0 such that f(x0) = x0. This is a deep theorem,  but one aspect of it is lovely, surprising, and entirely approachable by high-school geometry … Continue Reading ››

Danny’s Ellipse

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 interactive … Continue Reading ››

Logic Puzzles Made Visual

When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type: Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn't buy an apple or kale.Continue Reading ››

The Flying Squirrel-Frog Puzzle

While I enjoy reading The New York Times for its news coverage, I especially look forward to each Monday when they post a new math puzzle online in their Numberplay column. Several months ago, I shared a Numberplay puzzle from former Key Curriculum editor Dan Bennett. Now I'd like to recap the Numberplay puzzle … Continue Reading ››