How is a straight line/straight curve defined (in contexts where it is meaningful) ? I am trying to wrap my mind around this concept, but I can't understand it at all : how is straight-ness defined? is it defined ? or should I take it as an axiom, or just think about it at an intuitive level and say "a straight line is something that looks like this _____________" ? To clear things up a bit : is there a concrete synthetic definition of straightness that precisely describes something which looks like this ____ (beyond the circular attempts of algebraic/analytic geometry) ?