z-arcs in the thirty degrees sector
-
Yevgenya Movshovich
Abstract
In this detailed study of 3-segment non-convex simple arcs inscribed in the
Funding statement: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Acknowledgements
We are grateful to J. E. Wetzel for the continuous support through all stages of this study including revisions.
References
[1] P. Coulton and Y. Movshovich, Besicovitch triangles cover unit arcs, Geom. Dedicata 123 (2006), 79–88. 10.1007/s10711-006-9107-7Search in Google Scholar
[2] L. Moser, Poorly formulated unsolved problems in combinatorial geometry, mimeographed, 1966. Search in Google Scholar
[3] W. O. J. Moser, Problems, problems, problems, Discrete Appl. Math. 31 (2005), 201–225. 10.1016/0166-218X(91)90071-4Search in Google Scholar
[4] Y. Movshovich, Besicovitch triangles extended, Geom. Dedicata 159 (2012), 99–107. 10.1007/s10711-011-9648-2Search in Google Scholar
[5] Y. Movshovich, Λ-configuration and embedding, J. Geom. 111 (2020), no. 3, Paper No. 37. 10.1007/s00022-020-00549-0Search in Google Scholar
[6]
Y. Movshovich and J. E. Wetzel,
Drapeable unit arcs fit in the unit
[7] R. Norwood, G. Poole and M. Laidacker, The worm problem of Leo Moser, Discrete Comput. Geom. 7 (1992), no. 2, 153–162. 10.1007/BF02187832Search in Google Scholar
[8] C. Panraksa and W. Wichiramala, Wetzel’s sector covers unit arcs, Period. Math. Hungar. 2020 (2020), Article ID 62. 10.1007/s10998-020-00354-xSearch in Google Scholar
[9] J. E. Wetzel, Sectorial covers for curves of constant length, Canad. Math. Bull. 16 (1973), 367–375. 10.4153/CMB-1973-058-8Search in Google Scholar
[10] J. E. Wetzel, Fits and covers, Math. Mag. 76 (2003), no. 5, 349–363. 10.1080/0025570X.2003.11953209Search in Google Scholar
[11] J. E. Wetzel, Bounds for covers of unit arcs, Geombinatorics 22 (2013), no. 3, 116–126. Search in Google Scholar
[12]
J. E. Wetzel and W. Wichiramala,
A covering theorem for families of sets in
[13] J. E. Wetzel and W. Wichiramala, Sectorial covers for unit arcs, Math. Mag. 92 (2019), no. 1, 42–46. 10.1080/0025570X.2019.1523648Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps
- Perturbations on K-fusion frames
- Integral solutions of nondense impulsive conformable-fractional differential equations with nonlocal condition
- Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems
- Construction of complex potentials for multiply connected domain
- Solution of a transport equation with discontinuous coefficients
- Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets
- Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals
- Robust synchronization of chaotic fractional-order systems with shifted Chebyshev spectral collocation method
- M-projective curvature tensor on an (LCS)2n+1-manifold
- An adapted integration method for Volterra integral equation of the second kind with weakly singular kernel
- z-arcs in the thirty degrees sector
Articles in the same Issue
- Frontmatter
- Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps
- Perturbations on K-fusion frames
- Integral solutions of nondense impulsive conformable-fractional differential equations with nonlocal condition
- Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems
- Construction of complex potentials for multiply connected domain
- Solution of a transport equation with discontinuous coefficients
- Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets
- Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals
- Robust synchronization of chaotic fractional-order systems with shifted Chebyshev spectral collocation method
- M-projective curvature tensor on an (LCS)2n+1-manifold
- An adapted integration method for Volterra integral equation of the second kind with weakly singular kernel
- z-arcs in the thirty degrees sector
