Uploaded August 2020 | Updated September 2026, 1 week ago
And here is three-dimensional spherical space. Opposite points are not identified, but because of the weirdness of spherical perspective, point X is not only seen as point X, but is also seen as a mirage in -X (the opposite point in S^3).
So the sphere below our feet is real, and the sphere above is a mirage. The dogs walking there can scare us, but cannot attack us!
Earlier parts: https://t.co/IvqzMAbCA2 youtu.be/wm6fn9MfRKE
And here is three-dimensional spherical space. Opposite points are not identified, but because of the weirdness of spherical perspective, point X is not only seen as point X, but is also seen as a mirage in -X (the opposite point in S^3).
So the sphere below our feet is real, and the sphere above is a mirage. The dogs walking there can scare us, but cannot attack us!
Earlier parts: https://t.co/IvqzMAbCA2 youtu.be/wm6fn9MfRKE
![[360° VR] Portals to Non-Euclidean Geometries](https://i.ytimg.com/vi/bQSfzDugH7s/mqdefault.jpg "[360° VR] Portals to Non-Euclidean Geometries
This is a 360° VR version of our earlier video:https://www.youtube.com/watch?v=yqUv2JO2BCs
On this tour, portals will take us to various non-Euclidean geometries. This is not Minecraft!
A cool holonomy effect happened during this tour, but it was not explained by our guide Tehora! Have you found it? Please tell us in the comments!
Tehora Rogues channel: https://www.youtube.com/channel/UCHRkB4HgLLReBxWJwblHsjQ
Visited geometries:
* Three-dimensional Euclidean space 𝔼³ (cyan floors, music: Icy Land by Shawn Parrotee)
* Product space ℍ²×ℝ (green floors, music: Living Caves by Shawn Parrotee)
* Three-dimensional hyperbolic space ℍ³ (yellow floors, music: RLyeh by Shawn Parrotte)
* Product space 𝕊²×ℝ (blue floors, music: Ocean by Will Savino)
* Three-dimensional spherical space 𝕊³ (purple floors, music: Land of Eternal Motion by Shawn Parrotte)
* Solv (brownish floors, music: Lost Mountain by Lincoln Domina)
HyperRogue soundtrack under the Creative Commons BY-SA 3.0 license
Link to RogueViz: https://zenorogue.itch.io/rogueviz
To learn more about non-Euclidean geometry, play HyperRogue or visit our discord: https://discord.gg/8G44XkR")
