How can we visualize the process of adding or subtracting fractions with unlike denominators? The Web Sketchpad model below (and here) offers tools for representing fraction addition and subtraction on a number line as well as a parameter (called "divisions") that allows you to find a like denominator through visual inspection rather than calculation. [iframe … Continue Reading ››

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 … Continue Reading ››

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 … Continue Reading ››

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. … Continue Reading ››

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 – … Continue Reading ››

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 … Continue Reading ››

Attention Sketchpad fans: If you're a Mac user and would like to give the new Mac Sketchpad a spin, go ahead and contact me so that we can add you to our beta test. Several weeks ago, Apple released MacOS Catalina and brought an end to all 32-bit apps, including Sketchpad 5.06. Luckily, Nick … Continue Reading ››

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 … Continue Reading ››

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 … Continue Reading ››