Course Description

We explore the collection of rotations of three dimensional space.  In particular, we use a spherical puppet to start physically exploring SO(3), the set of spatial rotations. It quickly becomes clear that the larger shape of this space is very strange – and yet also somehow known to the human body intuitively and viscerally. In order to build a more logical intuition for this space, students will construct a spherical puppet of their own, which they use to solve a series of movement challenges, culminating in proof of the strangest property of SO(3), known as orientation entanglement: namely, that a 360 degree rotation will tangle up a set of strings, and yet a 720 degree rotation loops mysteriously brings everything back to its initial state. Even professional mathematicians can gain a newfound understanding of this phenomenon by personally going through these physical movement exercises. Finally, we introduce the algebra of the Quaternion numbers, which allows us to translate our movement-based discoveries into mathematically precise, formal statements that computers and robots can easily understand.