TITLE: What is a straight line?
QUESTION [5 upvotes]: I have researched this question for days and can not locate a good answer. It could be a mathematical object that is defined by an axiom as Euclid or Hilbert. But if a curve is drawn between two points can it be should using only the rules of plane geometry that the curve is a "straight line"? If the curve is not a straight line then does it follow that the theorems that rely on such a construction will not necessarily be valid? BTW I am speaking of Euclidean geometry only.

REPLY [3 votes]: When I was in Grammar School, our mathematics teacher defined a straight line as:
"The shortest connection between two points which, when extended to infinity in either direction can never intersect with itself."
This definition has always worked for me.