Geodesic
On the affine measurement of arcs of a moment curve
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1312-1333.

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The arc length, defined in affine space as an invariant of a unimodular transformation group, in the case of moment curve coincides with the result of the measurement process by successively putting off the unit of measure.
Keywords: moment curve, enica, affine center of arc on enica, affine length of arc.
Mots-clés : parabola, affine-equal arcs 
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I. V. Polikanova. On the affine measurement of arcs of a moment curve. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1312-1333. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a59/

[1] I.V. Polikanova, “On curves with affine-equivalent arcs”, MAR-2015: «Mathematics for Altai Region», a collection of papers of the All-Russian Conference on Mathematics (Barnaul, 2015), 34–38

[2] T. Flash, A.A. Handzel, “Affine differential geometry analysis of human arm movements”, Biological cybernetics, 96:6 (2007), 577–601 | DOI | MR | Zbl

[3] I.V. Polikanova, “Intersections of Polinomial Curves with Planes”, Izvestiya of Altai State University Journal, 4:96 (2017), 141–145

[4] I.V. Polikanova, “The canonical basis of enika”, MAR:«Mathematics for Altai Region», a collection of papers of the All-Russian Conference on Mathematics with international participation (Barnaul, 2018), 40–44

[5] I.V. Polikanova, “Asymptotic direction of enika”, Collection of scientific articles of the international conference «Lomonosov readings in Altai: Fundamental problems of science and education» (Barnaul, 2017), 317–320

[6] D. Davis, “Generic affine differential geometry of curves in $R^n$”, Proc. Roy. Soc. Edinburg Sect. A, Math., 136:6 (2006), 1195–1205 | DOI | MR | Zbl

[7] M. Berger, Geometry, Mir, M., 1984 | MR | Zbl

[8] L.S. Atanasian, V.T. Bazilev, Geometry, in 2 parts, v. 1, Knorus, M., 2015

[9] J. Favar, Course of local differential geometry, Librokom, M., 2010

[10] I.V. Polikanova, “Enika definiteness by a finite set of points”, MAR: «Mathematics for Altai Region», a collection of papers of the All-Russian Conference on Mathematics (Barnaul, 2017), 37–40

[11] L.S. Atanasian, V.T. Bazilev, Geometry, in 2 parts, v. 2, Knorus, M., 2015

[12] J.N. Clelland, E. Estrada, M. May, J. Miller, S. Peneyra, M. Schmidt, “A tail of two arc lengths: metric notions for curves in surfaces in equiaffine space”, Proceedings of the American Mathematical Society, 142:7 (2014), 2543–2558 | DOI | MR | Zbl