Mathematicians create warped worlds in virtual reality
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 arXiv.org preprint server.
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| David Dumas |
To explore the mathematical possibilities of alternative geometries, mathematicians imagine such ‘non-Euclidean’ spaces, where parallel lines can intersect or veer apart. Now, with the help of relatively affordable VR devices, researchers are making curved spaces — a counter-intuitive concept with implications for Einstein’s theory underlying gravity and also for seismology — more accessible. They may even uncover new mathematics in the process.
So far, there is not much to do in the eleVR world, apart from exploring tilings made of geometric shapes such as pentagons and dodecahedra. But the team plans to build hyperbolic houses and streets, as well as interactive experiences such as playing a non-Euclidean version of basketball. The researchers hope that their open-source software will become popular with science museums and the growing legion of consumer VR enthusiasts.
Others are bringing hyperbolic space to VR, too. Daan Michiels, a mathematician at the University of Illinois at Urbana–Champaign, developed a virtual hyperbolic universe as a student project in 2014. And David Dumas, a topologist at the University of Illinois in Chicago, and his students created a racquetball game in a virtual hyperbolic space, in which a ball sent in any direction eventually comes back to the starting point.
Virtual reality could soon join a long tradition of visualization and experimental tools that have helped mathematicians make discoveries. Visualizing fractals, for instance, led to discoveries about the underlying mathematics. “Figuring how to make use of [virtual reality] as a research tool is just starting now,” says Dumas.
Matsumoto says that the team would also like to create VR experiences for even more exotic geometries. In some such spaces, parallel lines might stay at a constant distance from each other if they go in one direction, but converge or diverge in another direction. And walking around a circle might lead to a place that’s up or down relative to the starting point, like going up or down a spiral staircase.
Visualizing such geometries could be especially useful as a mathematical tool, she says, because “very few people have thought of visualizing them at all”.
Source: Nature
Virtual reality could soon join a long tradition of visualization and experimental tools that have helped mathematicians make discoveries. Visualizing fractals, for instance, led to discoveries about the underlying mathematics. “Figuring how to make use of [virtual reality] as a research tool is just starting now,” says Dumas.
Matsumoto says that the team would also like to create VR experiences for even more exotic geometries. In some such spaces, parallel lines might stay at a constant distance from each other if they go in one direction, but converge or diverge in another direction. And walking around a circle might lead to a place that’s up or down relative to the starting point, like going up or down a spiral staircase.
Visualizing such geometries could be especially useful as a mathematical tool, she says, because “very few people have thought of visualizing them at all”.
Source: Nature
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