If we assume that Facebook was once the future of social media, the lines must have crossed at some point in the past. I believe that rules out hyperbolic space, as two lines which are parallel, will diverge in either direction. In an eliptic space, however, we must assume that time is circular and "parallel" lines in eliptic space will eventually cross each other, which means that Facebook would be the future of social media multiple times, which is not right. The only solution I can think of is that Facebook was never the future of social media and that Facebook exists in a euclidean space, which is to say that your assumption is correct. Q. E. D.