Tag Archives: Software

Conic Sections, Educational Technology, Math Software

Tweaking the Expanding Circle Construction

Leave a comment
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 ››
Conic Sections, Educational Technology, Math Software

The Expanding Circle Construction

Leave a comment
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 ››
Conic Sections, Educational Technology, Math Software

A Trio of Parabola Constructions

Leave a comment
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 ››
Advanced Mathematics, Educational Technology, Math Software

An Interactive Approach to Finding nth Roots

Leave a comment
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 ››
Educational Technology, Elementary Mathematics, Math Software

Beam of Light

Leave a comment
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. You … Continue Reading ››
Educational Technology, Geometry, Math Software

Catching Up with New Web Sketchpad Functionality

Leave a comment
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 ››
Conic Sections, Educational Technology, Math Software

The Folded Circle Construction

1 Comment
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 ››
Educational Technology, Geometry

A Double Spiral from David Henderson

8 Comments
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 ››