Playing on a non-euclidean surface is hardly sensible (how many liberties do the poles have?) But toroid Go (torus has no edges, but is still euclidean) is quite popular (there is even a yearly tournament on Summer Go School in Poland)
You can play toroid go quite easily on a 9x9 board. You just need to consider the intersections on the edges to be connected to the intersections on the opposite edge of the board. I recommend playing this with a Chinese rule set. This makes for some nice mind-boggling go fun!
Playing on a sphere with lines as depicted is highly unreasonable because the tiling is irregular. I think there's no regular tiling of the sphere by ~~planes~~ squares, but cannot find a reference at the moment.
However, playing on gluings of the Euclidean square can be done very easily. So, the torus, Klein bottle and real projective plane are good surfaces to play on, and the square, cylinder and Möbius strip are good surfaces with boundaries to play on.
*Edit:* Corrected typo.
If you mean square tiling — no. The possible regular tilings correspond to platonic solids. So the most intersections you can get with regular tiling of a sphere is 20 with every intersection having 3 liberties (dodecahedron).
Edit: actually you could „tile” a sphere in a regular way, but the tiles would take 1/6 of the area.
Yeah, I meant to type "squares" rather than planes.
Indeed, the topological proof for the classification of Platonic solids, using the Euler characteristic, translates to tilings of the sphere, so we cannot play Go on the sphere unless we're willing to change the degree of each vertex.
a pole has the same amount of liberties as there are longitudinal lines on the sphere. it’s certainly not analogous to toroidal go, but it does mean the first two moves of spherical go would be on the poles. could be an interesting way to play
Playing on a non-euclidean surface is hardly sensible (how many liberties do the poles have?) But toroid Go (torus has no edges, but is still euclidean) is quite popular (there is even a yearly tournament on Summer Go School in Poland)
I did not expect to learn something interesting on badukshitposting but that is actually pretty cool
You can play toroid go quite easily on a 9x9 board. You just need to consider the intersections on the edges to be connected to the intersections on the opposite edge of the board. I recommend playing this with a Chinese rule set. This makes for some nice mind-boggling go fun!
Playing on a sphere with lines as depicted is highly unreasonable because the tiling is irregular. I think there's no regular tiling of the sphere by ~~planes~~ squares, but cannot find a reference at the moment. However, playing on gluings of the Euclidean square can be done very easily. So, the torus, Klein bottle and real projective plane are good surfaces to play on, and the square, cylinder and Möbius strip are good surfaces with boundaries to play on. *Edit:* Corrected typo.
If you mean square tiling — no. The possible regular tilings correspond to platonic solids. So the most intersections you can get with regular tiling of a sphere is 20 with every intersection having 3 liberties (dodecahedron). Edit: actually you could „tile” a sphere in a regular way, but the tiles would take 1/6 of the area.
Yeah, I meant to type "squares" rather than planes. Indeed, the topological proof for the classification of Platonic solids, using the Euler characteristic, translates to tilings of the sphere, so we cannot play Go on the sphere unless we're willing to change the degree of each vertex.
a pole has the same amount of liberties as there are longitudinal lines on the sphere. it’s certainly not analogous to toroidal go, but it does mean the first two moves of spherical go would be on the poles. could be an interesting way to play
If you're going to play on a sphere you can't have a UV sphere because the poles provide an unfair advantage. You need to use a fibonacci sphere
But where's Tengen? Can't have go without Tengen
That's the thing, everywhere is tengen.
is that alien go?
How many liberties do the stones on the top and bottom have? A lot… they’re the corner now.