Geodesic

Our paper "Random triangles and polygons in the plane" was published recently in the American Mathematical Monthly. See this post about the preprint for more background, but the short version is that we give a novel answer to Lewis Carroll's question "What is the probability that a random triangle is obtuse?"

Above is an animated version of Figure 2 from the paper, showing a geodesic in triangle space. The geodesic starts at the equilateral triangle shown, and the three curved paths show the tracks of the three vertices.