Geometry & Topology: Matsumoto & Segerman -- Non-euclidean virtual reality

Non-euclidean virtual reality

Vi Hart, Andrea Hawksley, Sabetta Matsumoto and Henry Segerman

The properties of euclidean space seem natural and obvious to us, to the
point that it took mathematicians over two thousand years to see an
alternative to Euclid’s parallel postulate. The eventual discovery of
hyperbolic geometry in the 19th century shook our assumptions, revealing
just how strongly our native experience of the world blinded us from
consistent alternatives, even in a field that many see as purely
theoretical. Non-euclidean spaces are still seen as unintuitive and exotic,
but with direct immersive experiences we can get a better intuitive feel for
them. The latest wave of virtual reality hardware, in particular the HTC
Vive, tracks both the orientation and the position of the headset within a
room-sized volume, allowing for such an experience. We use this nacent
technology to explore the three-dimensional geometries of the
Thurston/Perelman geometrization theorem. This talk focuses on our
simulations of 3-dimensional hyperbolic space and the product of the 
hyperbolic plane with the euclidean line.

Participants will be able to experience simulations of these geometries first hand.