From a math point of view are interesting cause since are equations of third grade, any line in a projective space will intersect them in three points. That is

From a math point of view are interesting cause since are equations of third grade, any line in a projective space will intersect them in three points. That is the feature, it means they can define a binary operator that given two points returns a point, the third intersection with a line. This opens up a Pandora's gift.