# Tag Archives: Constructions

# The Varied Paths to Constructing a Rhombus

In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral.

# 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 ››

# Circle Tracer Challenges

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 … Continue Reading ››

# A Double Spiral from David Henderson

David Henderson, the author of *Experiencing Geometry*, 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, ways of … 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 … 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 ››

# Dissecting Rectangles Into Squares

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 ››

# A Geometry Gem from Twitter

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 ››