Projective geometry is a version of geometry in which there are points, lines, and planes, but in which there are no such things as distance or parallel lines.
You say that in projective geometry, there's no notion of distance -- but that's incorrect, I think. You can define a perfectly nice metric: given two projective points (= lines through the origin in R^2), the distance between them is the angle between them (take the smaller one). This is a metric, and so I can sensibly talk about the distance between projective points.
The "no parallel lines" is indeed correct and the entire reason that Dobble works, but I'm not clear on the distance part.
That’s true, but you can put a metric on anything, such as the discrete metric, so you would need to be more specific about what “nice” means. Wikipedia’s entry on “projective geometry” states that projective geometry is “an elementary non-metrical form of geometry, meaning that it does not support any concept of distance” and that “facts are independent of any metric structure“. My statement was a reference to this.
You say that in projective geometry, there's no notion of distance -- but that's incorrect, I think. You can define a perfectly nice metric: given two projective points (= lines through the origin in R^2), the distance between them is the angle between them (take the smaller one). This is a metric, and so I can sensibly talk about the distance between projective points.
The "no parallel lines" is indeed correct and the entire reason that Dobble works, but I'm not clear on the distance part.
That’s true, but you can put a metric on anything, such as the discrete metric, so you would need to be more specific about what “nice” means. Wikipedia’s entry on “projective geometry” states that projective geometry is “an elementary non-metrical form of geometry, meaning that it does not support any concept of distance” and that “facts are independent of any metric structure“. My statement was a reference to this.