caa a22 4500 44581327X CHVBK 20180317145218.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00022-011-0076-0 doi (NATIONALLICENCE)springer-10.1007/s00022-011-0076-0 A generalized Winternitz Theorem [Elektronische Daten] [Prosenjit Bose, Paz Carmi, Ferran Hurtado, Pat Morin] We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point $${q \in P}$$ such that every half-polygon that contains q contains nearly 1/2(k +1) times the area of P. We also give a family of examples showing that this result is the best possible. Springer Basel AG, 2011 Winternitz' Theorem nationallicence Centerpoint Theorem nationallicence Polygons nationallicence Bose Prosenjit School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada aut Carmi Paz Department of Computer Science, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut Hurtado Ferran Departament de Matemàtica Aplicada II, Universitat Politécnica de Catalunya (UPC), Edifici Omega, Campus Nord, Jordi Girona, 1-3, 08034, Barcelona, Spain aut Morin Pat School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada aut Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 29-35 0047-2468 100:1-2<29 2011 100 22 https://doi.org/10.1007/s00022-011-0076-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0076-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bose Prosenjit School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada aut NATIONALLICENCE 700 1- Carmi Paz Department of Computer Science, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel aut NATIONALLICENCE 700 1- Hurtado Ferran Departament de Matemàtica Aplicada II, Universitat Politécnica de Catalunya (UPC), Edifici Omega, Campus Nord, Jordi Girona, 1-3, 08034, Barcelona, Spain aut NATIONALLICENCE 700 1- Morin Pat School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 29-35 0047-2468 100:1-2<29 2011 100 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer