In Greek mathematics γραμμή still is defined as a continuous one-dimensional flow of points: curve, straight line, ... and the noun ευθεία is straight line (straight is never used as a noun in mathematics). In most of the mathematical world this has been changed: a line is today defined as a straight line. This means that line = ευθεία (or straight line if you want) but for γραμμή there is no simple translation any more???
By coincidence, this afternoon, I heard somebody helping a driver to park. He told «ευθεία» not «γραμμή». I thought he wanted to be accurate since the case was critical and I thought that maybe you would find this interesting. By the way when we want to say go straight we also say «πήγαινε ίσια» or in case of driving «ίσιωνε». Curiosities!
This really isn't true even outside of Greece. "Line" only means a straight line in mathematical/technical use. English speakers talk about "straight lines", "curved lines", "wavy lines", etc. all the time, just not in a mathematical context.
It's similar to the fact that "work" has an extremely specific meaning in physics, but it would be silly to claim that someone reading in their office could not be doing work, as they were exerting no net force over any distance.
wailu2014! This is outside Greece. The Greek mathematicians still follow
Euclid: a line has only length, no breadth or height.
Hence Euclid's lines include curves with straight lines as a special case. Sometimes between 1965 and 1975 this was changed so that a line now, always is a straight line. But not in Greece, to my great enjoy they follow Euclid.
My dear kirakrakra (truly what does it mean this nickname?) as you mentioned above for greeks LINE is «a continuous one-dimensional flow of points» that unites two points, and STRAIGHT LINE is the SHORTER LINE THAT UNITES THOSE POINTS. And if exists any other line that has the same length with the former then those two lines are identical point by point. I wrote all this for you personally kirakrakra because the whole thing is conceptual and has nothing to do with what we see and I think you would adore it (like me on the other hand).
Please fix this. Whatever "the straight" was supposed to mean in this context, it stretched beyond reasonable hear. The languages can't be translated with mathematical precision. We should learn from a living language translated to a living language; if I would ever be speaking like this "I see THE straight" I would sound like Google translate :-)