Geodesic
Criteria for the straightness of a curve
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 86-98.

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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.
Keywords: criterion for the straightness of a curve, curve with similar arcs, straight line, fractal curve, curve with affine equivalent arcs. 
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I. V. Polikanova. Criteria for the straightness of a curve. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 86-98. http://geodesic.mathdoc.fr/item/INTO_2023_220_a9/

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