2D line.
Distance.
The shortest path between two points
line segment
The shortest path between two points is called a geodesic. In flat (Euclidean) space it is simply a straight line.
difference between shortest path and alternate path
The shortest, most direct path between two points is linear.
The shortest, most direct path between two points is linear.
It is easier to design that way and straight lines are the shortest path between two points.
actually, there is, depending on your definition of polygon, and your definition of a line segment. A line segment is the shortest path btwn two points, right? So take a sphere and pick any two points on that sphere. The shortest path between them on the surface of the sphere would be a "curve" along the surface, but it's the shortest path between the points, so it technally is a line segment. Take two of these line segments that intersect at two points, and there is your two sided polygon!
Yes, on a plane surface (a flat sheet of paper, for example).
The shortest route between 2 points on the surface of a planet is a great circle route, which is a path that follows the circumference of a circle formed by the intersection of the planet's surface and a plane passing through its center. This route represents the shortest distance between the two points.