z-arcs in the thirty degrees sector

• Autorzy: Movshovich Yevgenya

Identyfikatory

DOI

10.1515/jaa-2021-2056

• Języki publikacji: EN

Abstrakty

EN

In this detailed study of 3-segment non-convex simple arcs inscribed in the 30∘ sector, we show that each such arc of length one fits in the interior of the sector of radius one with the prescribed embedding. We discuss implications of this study for covering problems involving triangular covers and for the worm problem of Leo Moser.

Słowa kluczowe

EN

unit arc; worm; worm cover; lambda configuration

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 2
• Strony: 299--320
• Opis fizyczny: Bibliogr. 13 poz., rys. kolor.

Twórcy

autor

Movshovich Yevgenya

• UIUC, 1409 W Green St., Urbana, IL 61801, USA

• https://orcid.org/0000-0003-2143-0168

Bibliografia

• [1] P. Coulton and Y. Movshovich, Besicovitch triangles cover unit arcs, Geom. Dedicata 123 (2006), 79-88.
• [2] L. Moser, Poorly formulated unsolved problems in combinatorial geometry, mimeographed, 1966.
• [3] W. O. J. Moser, Problems, problems, problems, Discrete Appl. Math. 31 (2005), 201-225.
• [4] Y. Movshovich, Besicovitch triangles extended, Geom. Dedicata 159 (2012), 99-107.
• [5] Y. Movshovich, Λ-configuration and embedding, J. Geom. 111 (2020), no. 3, Paper No. 37.
• [6] Y. Movshovich and J. E. Wetzel, Drapeable unit arcs fit in the unit 30∘ sector, Adv. Geom. 17 (2017), no. 4, 497-506.
• [7] R. Norwood, G. Poole and M. Laidacker, The worm problem of Leo Moser, Discrete Comput. Geom. 7 (1992), no. 2, 153-162.
• [8] C. Panraksa and W. Wichiramala, Wetzel’s sector covers unit arcs, Period. Math. Hungar. 2020 (2020), Article ID 62.
• [9] J. E. Wetzel, Sectorial covers for curves of constant length, Canad. Math. Bull. 16 (1973), 367-375.
• [10] J. E. Wetzel, Fits and covers, Math. Mag. 76 (2003), no. 5, 349-363.
• [11] J. E. Wetzel, Bounds for covers of unit arcs, Geombinatorics 22 (2013), no. 3, 116-126.
• [12] J. E. Wetzel and W. Wichiramala, A covering theorem for families of sets in ℝd, J. Comb. 1 (2010), no. 1, 69-75.
• [13] J. E. Wetzel and W. Wichiramala, Sectorial covers for unit arcs, Math. Mag. 92 (2019), no. 1, 42-46.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)