In my previous post
, I presented a number line model for adding fractions. Now, I'd like to offer an updated Web Sketchpad fraction model below (and here
) with two new pieces of functionality:
- You can subtract as well as add fractions.
- You can divide the number line into equal parts and choose the … Continue Reading ››
In previous posts, I've presented fraction-related websketches from the Dynamic Number
project. Several of these activities—specifically Dividing and Subdividing
and Deducing the Mystery Fraction
—focus on a number-line representation of fractions. Below (and here
) is another such websketch, with students constructing segments of fractional length that can be placed end to … Continue Reading ››
In my prior blog posts
, I've presented methods for constructing ellipses and parabolas using both Web Sketchpad and paper folding. Now it's time for me to finally turn my attention to hyperbolas.
All of the Web Sketchpad models below (and here
) are based on the distance definition of a hyperbola: the set of points … Continue Reading ››
When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped.
In this post, I'll describe a Web Sketchpad activity that … Continue Reading ››
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 ››
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 ››
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 ››
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 ››
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 ››
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 ››