The researchers built a VR landscape that followed the rules of hyperbolic geometry. Here, a screengrab of one of these non-Euclidean worlds in the research group’s simulations. | Credit: eleVR/Hypernom
Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where the usual rules of geometry and physics don’t apply.
Vi Hart, who founded the research group eleVR, led a team that built a virtual landscape that looks like a set of endlessly repeating chambers. This virtual landscape follows the rules of a type of non-Euclidean geometry called hyperbolic geometry (also called H-space). It operates in a different way than the normal world, which abides by so-called Euclidean geometry. In this VR universe, the floor can fall away from your feet as you walk forward and distances aren’t what they seem, all because lines and angles don’t behave the way they do in the ordinary world.
“In H-space, when you move your head a little bit it’s normal, but if you make larger movements it’s different,” Henry Segerman, a co-author of the studies and an assistant professor of mathematics at Oklahoma State University, told Live Science. That’s because in H-space “a lot of it is very close to you,” meaning that the amount of space between two points is less in certain directions than in Euclidean space, where a unit of distance is a consistent length.
The results have applications in the academic realm as well as for the video-game industry. However, the impetus for the project was more art than science: “Mathematics and art are not so distant from each other,” Hart said. “In both mathematics and art, we can talk about entirely fictional worlds.”
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Source: LiveScience