Tag Archives: Dynamic Geometry

A Trio of Parabola Constructions

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 … Continue Reading ››

An Interactive Approach to Finding nth Roots

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 ››

Catching Up with New Web Sketchpad Functionality

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 ››

The Folded Circle Construction

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 … Continue Reading ››

A Double Spiral from David Henderson

David Henderson, one of my two Cornell master's thesis advisors, died this past December. I wrote about David in a prior post, and in particular, his approach of asking us  to grapple with a small number of  rich problems, allowing us  to find our own, often non-traditional, … Continue Reading ››

What’s New with Web Sketchpad in 2019

For the past five years, Scott and I have featured interactive Web Sketchpad models in nearly all our Sine of the Times blog posts.  As much fun as it's been to build "websketches" to share with you, we've really wanted to put the creative power of Web Sketchpad into your hands. And now, finally, that's possible. Today … Continue Reading ››

A Dynamic Approach to Finding Pirate Treasure

In his 1947 book, One, Two, Three...Infinity, physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle.
Among a pirate's belongings you find the following note: The island where I buried my treasure contains a single palm tree. Find the tree. From the palm tree, … Continue Reading ››

The Scaled Maps Problem

Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other. Believe it or not, you can stick a pin straight through both maps … Continue Reading ››