# teaching machines

## University of Canterbury Seminar

Hi, I’m Chris and I teach people to teach machines. But I am a reluctant computer scientist. Sometimes I get concerned that the thing I know the most about is not directly linked to my survival. My father knew how to keep machines running. My wife grows vegetables. In a post-apocalyptic world, they would be […]

## 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 &=& […]

## 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 […]

## Sensing Shapes

In the late 1600s, William Molyneaux posed a question to a friend: Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and the other, which […]

## Stolen Rings

Recently, I stole something precious from a friend. I was sitting in Andy’s office, and there it was. An interesting shape. Three rings nestled inside each other. They could rotate independently, but if any translated, the others would follow. I had to have these rings. So, I stole them. Well, I stole the idea of […]

If you are an illustrator, there are two things that are harder to draw than anything else. The first is lettering. Bless you, illustrators, if you have to draw a busy street scene with lots of storefronts full of signs and words. The second is stars. Most illustrators just give up on stars. They are […]

## Flat Braid

When all you know of trees is that they have bark and leaves, you view the woods as a background to the more interesting foreground activity of a jog, or a campout, or a proposal. But when one knows the trees, it’s hard to not stop every few feet and shake hands with some old […]

## Icosahedron, Part 2

Several hours later, I have now found the difference between an octahedron and an icosahedron. I had been stuck on generating the coordinates of the octahedron. A little reading and experimentation directed my attention to the cube circumscribing the icosahedron. The way I’ve set things up, its vertices are all [±u, ±u, ±u], where u […]

## Icosahedron, Part 1

One of the important consequences of the internet is that we can now talk freely about icosahedrons. We’re not bound to the interests of those that are geographically near. We can love pretty much anything and find a community that shares our passions somewhere online. So, this morning, while I was trying to get other […]