The Math Education Blog
In my prior blog posts, I’ve presented methods for constructing ellipses and parabolas using both Web Sketchpad and paper folding. Now it’s time for me to finally turn my attention to hyperbolas. All of the Web Sketchpad models below (and here) are based on the distance definition of a hyperbola: the set of points P...
Mathematics is a wonderful game. It’s one that can stretch students’ minds and expose them to the beauty and unexpected delights that lie behind every good problem. I’ve always gravitated to colleagues who share my love of math’s playful, game-like side, so I quickly made friends with Toni Cameron when we met at P.S. 503...
When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped. In this post, I’ll describe a Web Sketchpad activity...
In last month’s blog post, I described a parabola construction technique dating back to the work of Persian polymath Ibn Sina (c. 970 – 1037). After I published the post, my colleague Scott noted that my construction could be more robust to allow for parabolas that are downward facing as well as upward facing. Such...
There can never be enough conic-section construction techniques—at least that’s my philosophy, having grown up to think that conics existed purely in the realm of algebraic equations. So to continue my conic section construction series on Sine of the Times, I’ll present a parabola construction attributed to Ibn Sina (Avicenna), a Persian polymath (c. 970 – 1037)...
In my prior blog posts, I’ve presented methods for constructing ellipses using Web Sketchpad and paper folding. The other conic sections are feeling a bit left out, so let’s explore some techniques for constructing parabolas. All three Web Sketchpad models below (and here) are based on the distance definition of a parabola: The set of...
When students find the nth roots of a complex number, they use de Moivre’s Theorem and a fair bit of calculation and trigonometry. In this blog post, I’m going to approach the topic from a more visual perspective and make use of the following geometric way to think about complex number multiplication: To multiply two complex...
This month’s post is based on a problem that appears in Martin Gardner’s Sixth Book of Mathematical Diversions from Scientific American. Below (and here) is a Web Sketchpad model of an orderly forest. There is a tree at every point whose x– and y-coordinates are both integers. These are the green points. You are standing...
This past January, we introduced the Web Sketchpad Tool Library and Viewer. The Tool Library is a collection of over 60 mathematical tools for customizing a Web Sketchpad model, making it possible for teachers to decide which tools students have available to them on an activity-by-activity basis. The Viewer is a site for students to...
Of all the conic section construction techniques, my favorite is undoubtedly the approach that requires nothing more than a paper circle. Here’s what to do: Draw or print a circle and its center, point A, on a sheet of paper. Cut out the circle. Mark a random point B anywhere on the circle. Then, fold...