Polar Graph
A year ago I decided to see if fifth graders could create shapes using polar coordinates. I bet myself that they could if we spent some time first traversing a polar grid, identifying the labels of the rings and the spokes. We didn’t think of them as angles and radii, because those semantics weren’t important […]
Phone Programming
Twoville now supports masking, which means we can subtract shapes from other shapes. Since I’m teaching a course on mobile app programming this semester, phones have been on my mind. Accordingly, here’s one of the first runs of the masking feature: In this code, hole is a container of other shapes that will be subtracted […]
Why 12?
We looked previously at how an octave—or doubling, as we called it—is partitioned non-linearly into intermediate tones. But we didn’t ultimately decide how many intermediate tones there should be. The pioneers of Western music converged on a 12-partition. But why not 8? Or 10? Or 11? Or 13? Ultimately, we want our instruments to sound […]
Droplets
A year ago some students and I started designing programming languages for generating 2D vector art. I called my language Twoville, which pays homage to Seymour Papert’s metaphor of learning math in Mathland just as we learn French in France. The language is a place to learn about and forge 2D shapes. After the semester […]
Twelve Steps
Music theory is a daunting subject, built out of centuries of mathematical analysis and aristocratic pride. Sometimes I think I’d be better off reinventing it than trying to learn it at this late stage of its maturity. Here’s how I might get started. One day I’d be absently fooling around with a bit of wire, […]
Parametric Puzzle
Check out these these parametric equations: $$\begin{array}{rll}x &=& \cos v \cdot \cos u \\y &=& \sin v \\z &=& \cos v \cdot \sin u\end{array}$$ Do you know what they do? They are most assuredly not magic. Here, let’s rename the variables, and you can try again: $$\begin{array}{rll}x &=& \cos \textit{latitude} \cdot \cos \textit{longitude} \\y &=& […]
Intervals in Deltaphone
For a few years now, schools and industry have been telling kids that they can code. They say the jobs are plentiful, and the salary is enviable—the workforce is waiting. The nobler agents of educational reform will also tell our kids that programming is a creative exercise that will make them better thinkers in other […]
Flatcaps in Libigl
Madeup’s dowel solidifier has one job: thicken a sequence of line segments into a solid. But what if the sequence isn’t a polyline, but rather a branching structure like a tree or a fork? One could model each branch as a separate dowel and hope that nobody looks too closely at the joints, but that’s […]
STEM in Education 2018 Workshop
Welcome to the notes for the Computational Making with Madeup workshop at STEM in Education 2018. It’s my hope that you read the abstract for this workshop, and you consent to our stated goals: In this interactive hands-on workshop, participants will learn to build models using Madeup and gain skills and resources they can use […]
Stepping Up in Deltaphone
Recently I added chords to Deltaphone, which required me to rethink how I was structuring the blocks to play notes. Previously, the play block came in two forms. There was a form for an absolutely-specified note, like “play C natural in the fourth octave.” And there was a form for a relatively-specified note, like “play […]