"If we were in it, we could see it, feel it or walk through it," Matsumoto said. If you consciously encountered hyperbolic geometry, you'd be capable of experiencing it. Accordingly, hyperbolic geometry was helpful in arriving at the Theory of Relativity, which describes realities of spacetime outside the habits of human perception, though not completely out of perceptual reach. It describes some actual physics, and is yet another example that there's more to reality than meets the eye.įor example, gravity from massive celestial bodies bends rays of light. Hyperbolic geometry isn't just hypothetical. And it gives the VR wearer a visual output that is Euclidean, i.e. Matsumoto and Segerman's new virtual reality program detects head motions in 3D Euclidean space and warps them into virtual movement in 3D hyperbolic space. And when you've warped the plane, it warps all of space at the same time.
That warp changes principles: Parallel lines curve away from each other triangles have warped lines, and there's no such thing as a rectangle as we know it. Since we usually live in a Euclidean reality, the warped plane would now look to us like a three-dimensional object, but it's still a plane, so it's really two-dimensional.
If you warp a Euclidean plane like a Pringle's potato chip, giving it hyperbolic curves, you get an idea of hyperbolic geometry. We recognize this geometry when we look at buildings, desks or coffee cups. "The virtual reality takes something that would normally live in a set of equations, and makes something you can interact with." "Visualizations can help to prove theorems that are purely abstract, and physicists want to get an intuition for what's going on," said Matsumoto, an assistant professor in Georgia Tech's School of Physics. Segerman and Matsumoto collaborated on the hyperbolic virtual reality experience with a collective of mathematician-artists called eleVR to make the work of the geometry experts easier and more productive. That weirdness can give the non-mathematician an idea of how picturing non-Euclidean geometries mentally can strain even the minds of mathematicians and physicists. Or you can peruse it on a computer in 2D using the arrow keys.īut be a little careful walking around the 3D version, as the hyperbolic space doesn't have a floor to provide visual balance orientation, and turning corners is very different from in everyday life. You can navigate it with your VR headset or smart phone via a webVR interface. In the meantime, if you'd like a peek at the warped rainbow weirdness yourself, go here: h3. We'll go into the difference between them in the next section. Most people have never consciously seen hyperbolic geometry, as opposed to Euclidean geometry, which is how we usually experience the world. "It never stops, just keeps going, and you never get to the back side of it." He slid around a diamond-like shape in VR hyperbolic space, describing it. "If you walk around in this space, things that started out horizontal and vertical become twisted and weird," Segerman said, as he donned a VR headset. When Matsumoto or her collaborator, mathematician Henry Segerman from Oklahoma State University, do that, they're actually exploring particular geometric nooks. Splashed in color, the virtual space's graphics can seduce even the most math-phobic mind to roam, crawl or slither about.
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