Category Archives: Math Software
The Expanding Circle Construction
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.
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 … Continue Reading ››
Mac Sketchpad Beta Test
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 ››
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 ››
Beam of Light
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. … 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 ››
Dividing and Subdividing
Given a strip of paper, how might you divide it into fourths without using a ruler? Undoubtedly, you'd fold the strip in half and then in half again to locate the quarter marks. Now suppose that your goal is to divide a strip into sixths. You might start by folding the strip into thirds and … Continue Reading ››