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Virtually Hyper

Visualization

A brightly-colored, fractal like octagonal geometry on a black background that repeats in all directions

In motion, hyperbolic geometry makes shapes warp around like reflections in a special kind of funhouse mirror. Want to try it? Steer your VR here: h3.hypernom.com.

By Ben Brumfield

This is hyperbolic space viewed through virtual reality. The VR program depicts hyperbolic geometry, which is a twist on more customary geometry and a departure from the realm of usual human perception.

The world we see day to day is described by Euclidean geometry, taught in high school, with its lines, planes, rectangles, and spheres. To picture hyperbolic geometric space in your mind, grab a plane and warp it like a potato chip, then apply that to all of space.

Or take the easy route and don a VR headset. It will take you to a reality where parallel lines curve away from each other, the angles of triangles don’t add up to 180 degrees, and customary rectangles don’t exist.

Hyperbolic geometry has aided insight into physical realities that bewilder conventional perception, like space-time warping from the Theory of Relativity.

This virtual reality headset program is a collaboration of Georgia Tech applied mathematician Sabetta Matsumoto, an assistant professor in the School of Physics; mathematician Henry Segerman from Oklahoma State University; and the eleVR research group. It translates head movements into movements in hyperbolic geometry and then translates that back into VR optics for physicists and mathematicians to see.

People don’t usually have an opportunity to see hyperbolic spaces. The colorful shapes help them do so.

Related: Warped Reality: Virtual Trip to Hyperbolic Space, March 30, 2017

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