Quadrilateral reptiles

Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triang...
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Autor*in:	Laczkovich, Miklós [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Tilings Reptiles Quadrilaterals

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Beiträge zur Algebra und Geometrie - Berlin : Springer, 1993, 64(2022), 4 vom: 19. Dez., Seite 945-967
Übergeordnetes Werk:	volume:64 ; year:2022 ; number:4 ; day:19 ; month:12 ; pages:945-967

Links:	Volltext

DOI / URN:	10.1007/s13366-022-00663-x

Katalog-ID:	SPR053365933

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allfields	10.1007/s13366-022-00663-x doi (DE-627)SPR053365933 (SPR)s13366-022-00663-x-e DE-627 ger DE-627 rakwb eng Laczkovich, Miklós verfasserin aut Quadrilateral reptiles 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213 Enthalten in Beiträge zur Algebra und Geometrie Berlin : Springer, 1993 64(2022), 4 vom: 19. Dez., Seite 945-967 (DE-627)320518159 (DE-600)2014219-5 2191-0383 nnns volume:64 year:2022 number:4 day:19 month:12 pages:945-967 https://dx.doi.org/10.1007/s13366-022-00663-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2022 4 19 12 945-967
spelling	10.1007/s13366-022-00663-x doi (DE-627)SPR053365933 (SPR)s13366-022-00663-x-e DE-627 ger DE-627 rakwb eng Laczkovich, Miklós verfasserin aut Quadrilateral reptiles 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213 Enthalten in Beiträge zur Algebra und Geometrie Berlin : Springer, 1993 64(2022), 4 vom: 19. Dez., Seite 945-967 (DE-627)320518159 (DE-600)2014219-5 2191-0383 nnns volume:64 year:2022 number:4 day:19 month:12 pages:945-967 https://dx.doi.org/10.1007/s13366-022-00663-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2022 4 19 12 945-967
allfields_unstemmed	10.1007/s13366-022-00663-x doi (DE-627)SPR053365933 (SPR)s13366-022-00663-x-e DE-627 ger DE-627 rakwb eng Laczkovich, Miklós verfasserin aut Quadrilateral reptiles 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213 Enthalten in Beiträge zur Algebra und Geometrie Berlin : Springer, 1993 64(2022), 4 vom: 19. Dez., Seite 945-967 (DE-627)320518159 (DE-600)2014219-5 2191-0383 nnns volume:64 year:2022 number:4 day:19 month:12 pages:945-967 https://dx.doi.org/10.1007/s13366-022-00663-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2022 4 19 12 945-967
allfieldsGer	10.1007/s13366-022-00663-x doi (DE-627)SPR053365933 (SPR)s13366-022-00663-x-e DE-627 ger DE-627 rakwb eng Laczkovich, Miklós verfasserin aut Quadrilateral reptiles 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213 Enthalten in Beiträge zur Algebra und Geometrie Berlin : Springer, 1993 64(2022), 4 vom: 19. Dez., Seite 945-967 (DE-627)320518159 (DE-600)2014219-5 2191-0383 nnns volume:64 year:2022 number:4 day:19 month:12 pages:945-967 https://dx.doi.org/10.1007/s13366-022-00663-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2022 4 19 12 945-967
allfieldsSound	10.1007/s13366-022-00663-x doi (DE-627)SPR053365933 (SPR)s13366-022-00663-x-e DE-627 ger DE-627 rakwb eng Laczkovich, Miklós verfasserin aut Quadrilateral reptiles 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213 Enthalten in Beiträge zur Algebra und Geometrie Berlin : Springer, 1993 64(2022), 4 vom: 19. Dez., Seite 945-967 (DE-627)320518159 (DE-600)2014219-5 2191-0383 nnns volume:64 year:2022 number:4 day:19 month:12 pages:945-967 https://dx.doi.org/10.1007/s13366-022-00663-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2022 4 19 12 945-967
language	English
source	Enthalten in Beiträge zur Algebra und Geometrie 64(2022), 4 vom: 19. Dez., Seite 945-967 volume:64 year:2022 number:4 day:19 month:12 pages:945-967
sourceStr	Enthalten in Beiträge zur Algebra und Geometrie 64(2022), 4 vom: 19. Dez., Seite 945-967 volume:64 year:2022 number:4 day:19 month:12 pages:945-967
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Tilings Reptiles Quadrilaterals
isfreeaccess_bool	true
container_title	Beiträge zur Algebra und Geometrie
authorswithroles_txt_mv	Laczkovich, Miklós @@aut@@
publishDateDaySort_date	2022-12-19T00:00:00Z
hierarchy_top_id	320518159
id	SPR053365933
language_de	englisch
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author	Laczkovich, Miklós
spellingShingle	Laczkovich, Miklós misc Tilings misc Reptiles misc Quadrilaterals Quadrilateral reptiles
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topic_title	Quadrilateral reptiles Tilings (dpeaa)DE-He213 Reptiles (dpeaa)DE-He213 Quadrilaterals (dpeaa)DE-He213
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title	Quadrilateral reptiles
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title_full	Quadrilateral reptiles
author_sort	Laczkovich, Miklós
journal	Beiträge zur Algebra und Geometrie
journalStr	Beiträge zur Algebra und Geometrie
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title_sort	quadrilateral reptiles
title_auth	Quadrilateral reptiles
abstract	Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. © The Author(s) 2022
abstractGer	Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. © The Author(s) 2022
abstract_unstemmed	Abstract A polygon P is called a reptile, if it can be decomposed into %$k\ge 2%$ nonoverlapping and congruent polygons similar to P. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of Betke and Osburg we find that every convex reptile is a triangle or a trapezoid. © The Author(s) 2022
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title_short	Quadrilateral reptiles
url	https://dx.doi.org/10.1007/s13366-022-00663-x
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Quadrilateral reptiles

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