Check out Janggi (Korean Chess), our featured variant for December, 2024.


[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Single Comment

Chess on an Infinite Plane. Chess game with no boundaries (infinite board), and Guard, Chancellor, and Hawk. () [All Comments] [Add Comment or Rating]
H. G. Muller wrote on Mon, Aug 7, 2023 08:14 AM UTC in reply to Aurelian Florea from Sun Aug 6 10:18 AM:

I could not realize yet if this yields a rider where the branches don't interesect each other.

Isn't that obvious? To intersect they would need to have the same ratio of n and m. But there is only a single irreducible representation of n/m. (In other words, if n/m = n'/m' then nm' = n'm, and have the same factors. But since none of the factors in n is in m, they must all be in n', and none of the factors in n' is in m', and must be in n. So n = n'. This relies on the factorization of a number to be unique.)