Criteria for the straightness of a curve

Abstract

The following three criteria for the straightness of the a are proved:

1. A curve in an affine n-dimensional space is rectilinear if and only if each of its chords has a common point with the arc contracted by it, which is different from their common ends.
2. A curve in a Euclidean 3-dimensional space is rectilinear if and only if any two of its oriented arcs are similar.
3. A rectifiable curve in a Euclidean n-dimensional space is rectilinear if and only if any two of its oriented arcs are similar.