*A,*on a sheet of paper. Cut out the circle. Mark a random point

*B*anywhere on the circle. Then, fold … Continue Reading ››

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 ››

Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.

On page 1 of the websketch below (and here), begin by asking students to drag point … Continue Reading ››
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 ››

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 ››

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 picture below on the left shows a right triangle *JML* with altitude *KM*. This altitude is defined as the *geometric mean* of *JK* and *KL*. Using similar triangles, you can prove that *JK* × *KL* = *KM*². Another way to think about this construction is shown below on the right. Start with segments *JK* and … Continue Reading ››

Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem presented the image below with two squares, *ABCD* and *BFGE,* sharing a vertex. Given that *AE* = 5, what is the length of *DG?*
My first thought was that surely the problem was … Continue Reading ››

As a longtime Sketchpad fan, one of the most interesting features of Web Sketchpad (WSP) for me is the way its behavior can be customized. WSP makes it possible to add JavaScript to a web page in order to interact directly with objects in the sketch. For instance, a JavaScript function could use the locations … Continue Reading ››

At the 2017 NCTM Annual Meeting I was invited to do a short Wednesday-afternoon presentation on Function Dances in the NCTM Networking Lounge. (Here's the handout from the presentation.)
The idea of function dances is to get students (or in this case teachers) moving around, acting as the independent and dependent … Continue Reading ››

In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››