When you curve the line you are travelling you are no longer going directly from one point to the other. If you want to go from one point to another you would want to go directly to the second point.
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The shortest distance between two points is... a straight line.
A straight line is the shortest distance between two points, a line is the delineation of a connection between two or more points.
In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.
In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.
You get a curve. If you join them along the shortest [Euclidean] distance between them, you get a straight line.