Visualizing geometries

Mathematicians create warped worlds in virtual reality

“It feels like the entire universe is within a sphere that is maybe within a couple metres’ radius,” says topologist Henry Segerman at Oklahoma State University in Stillwater. He is describing, not an LSD trip, but his experience of exploring a curved universe in which the ordinary rules of geometry do not apply. Segerman and his collaborators have released software allowing anyone with a virtual-reality (VR) headset to wander through this warped world, which they previewed last month in two papers on the preprint server. To explore the mathematical possibilities of alternative geometries, mathematicians imagine such ‘non-Euclidean’ spaces, where parallel lines can intersect or veer apart. ….[READ]