The count matroid characterizing the collection of edge lengths in a planar bar and joint framework due to Pollaczek-Geiringer and Laman is widely-known. Less heralded is the fact that the edge directions (or bearings) of a planar framework define the very same matroid. This result goes back at least to a 1987 book chapter by Whiteley and was reproved in 2003 by Martin using algebraic geometry. Their techniques give insight into an even less-studied matroid defined by the angles between pairs of edges.

In this talk we will discuss some new results about that angle matroid. We will also develop some angle analogs of rigidity-theoretic concepts like Laman numbers, circuits, and the pure condition. This is based on joint work with Sean Dewar, Georg Grasseger, Anthony Nixon, William Sims, Meera Sitharam, and David Urizar.