Watch a mathematician explore non-euclidian geometry with a VR headset

Mathematician Henry Sagerman and colleagues developed a cool way to observe non-euclidian geometry from a new vantage point: inside the geometry itself via virtual reality.

Via their paper on the project:

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 we believe that with direct immersive experience we can get a better “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.

Non-euclidean virtual reality (YouTube / Henry Segerman)