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Volumn 31, Issue 3, 2005, Pages 219-236

The Erdös-Nagy theorem and its ramifications

Author keywords

Computational geometry; Convexification; Curve inflation; Flips; Flipturns; Knot theory; Molecular reconfiguration; Pivots; Polygonal linkages; Polygons; Polymer physics; Robotics; Self avoiding walks

Indexed keywords


EID: 84867967318     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2004.12.005     Document Type: Article
Times cited : (16)

References (53)
  • 7
    • 33646614342 scopus 로고    scopus 로고
    • Polygons needing many flipturns
    • Department of Computer Science, University of Waterloo
    • T.C. Biedl, Polygons needing many flipturns, Technical Report CS-2000-04, Department of Computer Science, University of Waterloo, 2000
    • (2000) Technical Report CS-2000-04
    • Biedl, T.C.1
  • 8
    • 77955426540 scopus 로고
    • On the finiteness of the number of reflections that change a nonconvex plane polygon into a convex one
    • In Russian
    • R.H. Bing, and N.D. Kazarinoff On the finiteness of the number of reflections that change a nonconvex plane polygon into a convex one Matematicheskoe Prosveshchenie 6 1961 205 207 In Russian
    • (1961) Matematicheskoe Prosveshchenie , vol.6 , pp. 205-207
    • Bing, R.H.1    Kazarinoff, N.D.2
  • 9
    • 1542575510 scopus 로고    scopus 로고
    • Nontrivial embeddings of polygonal intervals and unknots in 3-space
    • J. Cantarella, and H. Johnston Nontrivial embeddings of polygonal intervals and unknots in 3-space J. Knot Theory Ramifications 7 8 1998 1027 1039
    • (1998) J. Knot Theory Ramifications , vol.7 , Issue.8 , pp. 1027-1039
    • Cantarella, J.1    Johnston, H.2
  • 12
    • 0012962476 scopus 로고
    • Solution of problem 3763
    • B. de Sz.-Nagy Solution of problem 3763 Amer. Math. Monthly 46 1939 176 177
    • (1939) Amer. Math. Monthly , vol.46 , pp. 176-177
    • De Sz.-Nagy, B.1
  • 14
    • 0040340046 scopus 로고
    • Problem number 3763
    • P. Erds Problem number 3763 Amer. Math. Monthly 42 1935 627
    • (1935) Amer. Math. Monthly , vol.42 , pp. 627
    • Erds, P.1
  • 19
    • 0012915578 scopus 로고
    • How to convexify a polygon
    • B. Grünbaum How to convexify a polygon Geombinatorics 5 1995 24 30
    • (1995) Geombinatorics , vol.5 , pp. 24-30
    • Grünbaum, B.1
  • 20
    • 0035965435 scopus 로고    scopus 로고
    • Convexification of polygons by flips and by flipturns
    • B. Grünbaum, and J. Zaks Convexification of polygons by flips and by flipturns Discrete Math. 241 2001 333 342
    • (2001) Discrete Math. , vol.241 , pp. 333-342
    • Grünbaum, B.1    Zaks, J.2
  • 21
    • 77955413747 scopus 로고
    • Problem 2: Konvexieren von Polygonen
    • T. Kaluza Problem 2: Konvexieren von Polygonen Math. Semesterber. 28 1981 153 154
    • (1981) Math. Semesterber. , vol.28 , pp. 153-154
    • Kaluza, T.1
  • 22
    • 0030267988 scopus 로고    scopus 로고
    • The symplectic geometry of polygons in euclidean space
    • M. Kapovich, and J.J. Millson The symplectic geometry of polygons in euclidean space J. Differential Geom. 44 1996 479 513
    • (1996) J. Differential Geom. , vol.44 , pp. 479-513
    • Kapovich, M.1    Millson, J.J.2
  • 24
    • 84867991927 scopus 로고
    • A finite number of reflections render a nonconvex plane polygon convex
    • N.D. Kazarinoff, and R.H. Bing A finite number of reflections render a nonconvex plane polygon convex Notices Amer. Math. Soc. 6 1959 834
    • (1959) Notices Amer. Math. Soc. , vol.6 , pp. 834
    • Kazarinoff, N.D.1    Bing, R.H.2
  • 25
    • 51249165461 scopus 로고
    • Reconfiguring closed polygonal chains in euclidean d-space
    • W.J. Lenhart, and S.H. Whitesides Reconfiguring closed polygonal chains in euclidean d-space Discrete Comput. Geom. 13 1995 123 140
    • (1995) Discrete Comput. Geom. , vol.13 , pp. 123-140
    • Lenhart, W.J.1    Whitesides, S.H.2
  • 26
    • 0000294335 scopus 로고
    • Monte Carlo generation of self-avoiding walks with fixed endpoints and fixed length
    • N. Madras, A. Orlitsky, and L.A. Shepp Monte Carlo generation of self-avoiding walks with fixed endpoints and fixed length J. Statist. Phys. 58 1990 159 183
    • (1990) J. Statist. Phys. , vol.58 , pp. 159-183
    • Madras, N.1    Orlitsky, A.2    Shepp, L.A.3
  • 28
    • 5944256461 scopus 로고
    • The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk
    • N. Madras, and A.D. Sokal The pivot algorithm: a highly efficient Monte Carlo method for the self-avoiding walk J. Statist. Phys. 50 1988 109 186
    • (1988) J. Statist. Phys. , vol.50 , pp. 109-186
    • Madras, N.1    Sokal, A.D.2
  • 29
    • 0018739525 scopus 로고
    • A linear algorithm for finding the convex hull of a simple polygon
    • D. McCallum, and D. Avis A linear algorithm for finding the convex hull of a simple polygon Inform. Process. Lett. 9 1979 201 206
    • (1979) Inform. Process. Lett. , vol.9 , pp. 201-206
    • McCallum, D.1    Avis, D.2
  • 31
    • 0023330010 scopus 로고
    • On-line construction of the convex hull of a simple polyline
    • A. Melkman On-line construction of the convex hull of a simple polyline Inform. Process. Lett. 25 1987 11 12
    • (1987) Inform. Process. Lett. , vol.25 , pp. 11-12
    • Melkman, A.1
  • 32
    • 0038049577 scopus 로고
    • Knotting of regular polygons in 3-space
    • K. Millett Knotting of regular polygons in 3-space J. Knot Theory Ramifications 3 1994 263 278
    • (1994) J. Knot Theory Ramifications , vol.3 , pp. 263-278
    • Millett, K.1
  • 33
  • 37
    • 77955413432 scopus 로고
    • On a method of transforming a nonconvex polygonal line into a convex one
    • In Russian
    • Yu.G. Reshetnyak On a method of transforming a nonconvex polygonal line into a convex one Uspehi Mat. Nauk 12 3 1957 189 191 In Russian
    • (1957) Uspehi Mat. Nauk , vol.12 , Issue.3 , pp. 189-191
    • Reshetnyak, Yu.G.1
  • 40
    • 0000500980 scopus 로고
    • Stretching chords of space curves
    • G.T. Sallee Stretching chords of space curves Geom. Dedicata 2 1973 311 315
    • (1973) Geom. Dedicata , vol.2 , pp. 311-315
    • Sallee, G.T.1
  • 41
    • 84867986206 scopus 로고    scopus 로고
    • Convexifying polygons in 3d: A survey
    • M. Soss, and G.T. Toussaint Convexifying polygons in 3d: a survey Contemp. Math. 304 2002 269 285
    • (2002) Contemp. Math. , vol.304 , pp. 269-285
    • Soss, M.1    Toussaint, G.T.2
  • 42
    • 24844477581 scopus 로고
    • Polygons and stars in a slit geometry
    • C.E. Soteros, and S.G. Whittington Polygons and stars in a slit geometry J. Phys. A 21 1988 L857 L861
    • (1988) J. Phys. A , vol.21
    • Soteros, C.E.1    Whittington, S.G.2
  • 43
    • 0001442577 scopus 로고
    • Efficient computer simulation of polymer conformation. I. Geometric properties of the hard-sphere model
    • S.D. Stellman, and P.J. Gans Efficient computer simulation of polymer conformation. I. Geometric properties of the hard-sphere model Macromolecules 5 1972 516 526
    • (1972) Macromolecules , vol.5 , pp. 516-526
    • Stellman, S.D.1    Gans, P.J.2
  • 44
    • 34249835757 scopus 로고
    • A chord stretching map of a convex loop is an isometry
    • J. Strantzen, and J. Brooks A chord stretching map of a convex loop is an isometry Geom. Dedicata 41 1992 51 62
    • (1992) Geom. Dedicata , vol.41 , pp. 51-62
    • Strantzen, J.1    Brooks, J.2
  • 48
    • 0038805561 scopus 로고    scopus 로고
    • Simple proofs of a geometric property of four-bar linkages
    • G.T. Toussaint Simple proofs of a geometric property of four-bar linkages Amer. Math. Monthly 110 6 2003 482 494
    • (2003) Amer. Math. Monthly , vol.110 , Issue.6 , pp. 482-494
    • Toussaint, G.T.1
  • 49
    • 0012913185 scopus 로고
    • The pivot algorithm and polygons: Results on the FCC lattice
    • E.J. Janse van Rensburg, S.G. Whittington, and N. Madras The pivot algorithm and polygons: results on the FCC lattice J. Phys. A 23 1990 1589 1612
    • (1990) J. Phys. A , vol.23 , pp. 1589-1612
    • Janse Van Rensburg, E.J.1    Whittington, S.G.2    Madras, N.3
  • 50
    • 0042324574 scopus 로고
    • Partial inflation of closed polygons in the plane
    • B. Wegner Partial inflation of closed polygons in the plane Contributions to Algebra and Geometry 34 1 1993 77 85
    • (1993) Contributions to Algebra and Geometry , vol.34 , Issue.1 , pp. 77-85
    • Wegner, B.1
  • 51
    • 52549103862 scopus 로고    scopus 로고
    • Chord-stretched convex versions of planar curves with self-intersections
    • Department of Mathematics, Technical University of Berlin
    • B. Wegner, Chord-stretched convex versions of planar curves with self-intersections, Technical Report, Department of Mathematics, Technical University of Berlin, 1999
    • (1999) Technical Report
    • Wegner, B.1
  • 52
    • 0041323033 scopus 로고
    • Self-avoiding walks with geometrical constraints
    • S.G. Whittington Self-avoiding walks with geometrical constraints J. Statist. Phys. 30 2 1983 449 456
    • (1983) J. Statist. Phys. , vol.30 , Issue.2 , pp. 449-456
    • Whittington, S.G.1
  • 53
    • 77955414886 scopus 로고
    • A property of simply-connected nonconvex polygons
    • In Russian
    • A.Ya. Yusupov A property of simply-connected nonconvex polygons Uchen. Zapiski Buharsk. Gos. Pedagog. 1957 101 103 In Russian
    • (1957) Uchen. Zapiski Buharsk. Gos. Pedagog. , pp. 101-103
    • Yusupov, A.Ya.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.