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Volumn 12, Issue 1, 2002, Pages 81-88

A direct proof of a theorem of Blaschke and Lebesgue

Author keywords

constant width; convex body; Reuteaux

Indexed keywords


EID: 84867961215     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02930861     Document Type: Article
Times cited : (20)

References (20)
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  • 2
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    • Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts
    • JFM 45.0731.04 10.1007/BF01458221 1511839
    • W. Blaschke 1915 Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts Math. Ann. 76 504 513 JFM 45.0731.04 10.1007/BF01458221 1511839
    • (1915) Math. Ann. , vol.76 , pp. 504-513
    • Blaschke, W.1
  • 5
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    • Minimum problems for volumes of constant bodies
    • P. Marcellini G. Talenti E. Visintin (eds). Marcel-Dekker New York
    • Campi, S.; Colesanti, A.; and Gronchi, P. Minimum problems for volumes of constant bodies, inPartial Diferential Equations and Applications, Marcellini, P.; Talenti, G.; and Visintin, E.; Eds.; Marcel-Dekker, New York, 43-55, (1996).
    • (1996) Partial Diferential Equations and Applications , pp. 43-55
    • Campi, S.1    Colesanti, A.2    Gronchi, P.3
  • 6
    • 0001919909 scopus 로고
    • Convex bodies of constant width
    • P.M. Gruber J.M. Wills (eds). Birkhäuser Basel
    • Chakerian, G.D. and Groemer, H. Convex bodies of constant width, inConvexity and its Applications, Gruber, P.M. and Wills, J.M.; Eds.; Birkhäuser, Basel, 49-96, (1983).
    • (1983) Convexity and Its Applications , pp. 49-96
    • Chakerian, G.D.1    Groemer, H.2
  • 7
    • 0011451086 scopus 로고
    • A proof of Blaschke's theorem on the Reuleaux triangle
    • 0048.16604 10.1093/qmath/3.1.296 51543
    • H.G. Eggleston 1952 A proof of Blaschke's theorem on the Reuleaux triangle Quart. J. Math. Oxford 3 2 296 297 0048.16604 10.1093/qmath/3.1.296 51543
    • (1952) Quart. J. Math. Oxford , vol.3 , Issue.2 , pp. 296-297
    • Eggleston, H.G.1
  • 9
    • 84972491774 scopus 로고
    • Isoperimetric ratios of Reuleaux polygons
    • Isoperimetric ratios of Reuleaux polygons,Pacific J. Math.,10, 823-829, (1960).
    • (1960) Pacific J. Math. , vol.10 , pp. 823-829
  • 10
    • 84867978989 scopus 로고
    • Analytic proof of Blaschke's theorem on the curve of constant breadth with minimum area i and II
    • JFM 53.0656.01 1568234 10.3792/pia/1195581847
    • M. Fujiwara 1927 Analytic proof of Blaschke's theorem on the curve of constant breadth with minimum area I and II Proc. Imp. Acad. Japan 3 307 309 JFM 53.0656.01 1568234 10.3792/pia/1195581847
    • (1927) Proc. Imp. Acad. Japan , vol.3 , pp. 307-309
    • Fujiwara, M.1
  • 11
    • 0030159597 scopus 로고    scopus 로고
    • An optimal control formulation of the Blaschke-Lebesgue theorem
    • 0857.52001 10.1006/jmaa.1996.0208 1391153
    • M. Ghandehari 1996 An optimal control formulation of the Blaschke-Lebesgue theorem J. Math. Anal. Appl. 200 322 331 0857.52001 10.1006/jmaa.1996.0208 1391153
    • (1996) J. Math. Anal. Appl. , vol.200 , pp. 322-331
    • Ghandehari, M.1
  • 13
    • 84868004339 scopus 로고    scopus 로고
    • Was ist eine runde Sache
    • 1022.00007 1650489
    • B. Kawohl 1998 Was ist eine runde Sache Mitt Ges. Angew. Math. Mech. 21 43 56 1022.00007 1650489
    • (1998) Mitt Ges. Angew. Math. Mech. , vol.21 , pp. 43-56
    • Kawohl, B.1
  • 14
    • 0011406746 scopus 로고
    • Sur le problème des isopérimètres et sur les domaines de larguer constante
    • H. Lebesgue 1914 Sur le problème des isopérimètres et sur les domaines de larguer constante Bull. Soc. Math. France C. R. 7 72 76
    • (1914) Bull. Soc. Math. France C. R. , vol.7 , pp. 72-76
    • Lebesgue, H.1
  • 15
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    • Sur quelques questions des minimums, relatives aux courbes orbiformes, et sur les rapports avec le calcul de variations
    • H. Lebesgue 1921 Sur quelques questions des minimums, relatives aux courbes orbiformes, et sur les rapports avec le calcul de variations J. Math. Pure Appl. 4 8 67 96
    • (1921) J. Math. Pure Appl. , vol.4 , Issue.8 , pp. 67-96
    • Lebesgue, H.1
  • 16
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    • Minkowski, H.1
  • 17
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    • Springer Lecture Notes in Mathematics Springer Berlin 0138.05101
    • Müller, K.Spherical Harmonics, Springer Lecture Notes in Mathematics, 17, Springer, Berlin, (1966).
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  • 19
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    • (1994) Convexity
    • Webster, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.