Mathematicians at Oklahoma State University and the Georgia Institute of Technology are attempting to bring a different world to life within virtual reality (VR) by creating a VR space to explore ‘alternative geometries’ in which the rules as we usually understand them do not apply.
In normal geometry as it is customarily taught, two parallel lines will continue on forever at the same distance apart, neither getting closer of further away. In non-euclidean geometry, though, those same parallel lines can eventually intersect, or veer apart.
Elisabetta Matsumoto, from the Georgia Institute of Technology and Henry Segerman at Oklahoma State University are working on a project called Hyperbolic VR, a collaborative effort to teach the public about hyperbolic geometry, a type of non-euclidean geometry in which a pair of parallel lines can diverge away from each other. “You can think about it, but you don’t get a very visceral sense of this until you actually experience it,” says Elisabetta Matsumoto.
The current version of the hyperbolic world that has been created doesn’t have very much to do just yet, other than allow users to wander around, but the team is planning on creating hyperbolic houses and streets within the VR world, and even building a non-Euclidian version of Basketball.
Playing sports in non-Euclidean space is not entirely new, as previously a topologist at the University of Illinois in Chicago called David Dumas produced a VR racquetball game with the help of his students, in which a ball hit in any direction will eventually return to its starting point.
“Figuring how to make use of [VR] as a research tool is just starting now,” says Dumas. Using visualisations of mathematical principals have helped to make discoveries before, such as when using visual interpretations of fractals lead to a better understanding of the underlying mathematics.