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If you're interested in this, you may be interested in Hyperbolica, which is a whole game about this concept:

https://store.steampowered.com/app/1256230/Hyperbolica/

https://www.youtube.com/watch?v=EMKLeS-Uq_8



Hyperbolica is mostly about the opposite, a hyperbolic universe, but there may be some section to the game that will be in a spherical universe. There's definitely some devlog video set in a spherical universe: https://www.youtube.com/watch?v=yY9GAyJtuJ0 The end of the video suggests this will be in the final game, at least as the time that video's creation.

In the meantime, the video I link is basically a video exploration of spherical geometry. One of the better ones, in my opinion, because it has "normal" objects in it, rather than floating heads or a ton of Earths or something.

(Another amusing sidebar: As you can see in the video above, an inhabitant of that space would be naturally inclined to say the space curves in above them. It would take an Einstein to assert that it's actually flat, and Spherical Einstein would have a very hard time describing "flat" to anyone. You can only make things "flat" contingent on the observer being in a very particular place. If you look at the next devlog: https://www.youtube.com/watch?v=pXWRYpdYc7Q back in Hyperbolic space, you can also see that a resident of that space would naturally believe the space they are in is a sphere (albeit one of variable radius, which is weird, but still, you can look out in the world and see the curvature, obviously it's round), and it would again take an Einstein to say that it is flat. It's flat if you are exactly on the ground, but hyperbolic space exaggerates any degree to which you are above the ground to make the horizon look round.)



These are great!

(There's also miegakure: https://www.youtube.com/watch?v=uWsBnVtl8tA )

I can't wait for these games to start being built for VR. Maybe it'll be possible to develop a sense for higher dimensionality intuitively using our senses.

Maybe young mathematicians and physicists can explore higher dimensions in VR to get accustomed to it, which might help with their theorizing and explorations.


Hyperbolica is to have VR support too, the creator discussed [0] how he had to use a specific technique to ensure the rendering was compatible with VR optimizations.

[0]: https://youtu.be/rBr-0bHQfxc?t=357


Looks like 4D toys is VR-supported: https://store.steampowered.com/app/619210/4D_Toys/



Antichamber has lots of weird, cool stuff in it, but nothing to do with non-Euclidean geometry. (They just use the term incorrectly.)


'Nother 4Dgame. An old classic, just get the ball out of the (hyper)cube.

http://harmen.vanderwal.eu/hypercube/


Specifically, the video about spherical geometry: https://www.youtube.com/watch?v=yY9GAyJtuJ0


Sokyokuban, a non-euclidean sokoban

https://news.ycombinator.com/item?id=25892889


What happens when cats appear?




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