In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using an overline (vinculum) above the symbols for the two endpoints, such as in AB.
historical image – create a line segment (1699)
In mathematics, a curve is an object similar to a line, but that does not have to be straight.
Megalithic art from Newgrange showing an early interest in curves
A dragon curve with a positive area