%0 Journal Article %T The Small Octagons of MaximalWidth %+ Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications (ENSEEIHT) %+ Algorithmes Parallèles et Optimisation (IRIT-APO) %+ Lab-STICC_ENSTAB_CID_IHSEV ; OSM %A Audet, Charles %A Hansen, Pierre %A Messine, Frédéric %A Ninin, Jordan %Z WOS %< avec comité de lecture %@ 0179-5376 %J Discrete and Computational Geometry %I Springer Verlag %V 49 %N 3 %P 589-600 %8 2013-04-01 %D 2013 %R 10.1007/s00454-013-9489-x %K Polygon %K Diameter %K Width %K Octagon %Z Mathematics [math]/Algebraic Geometry [math.AG] %Z Computer Science [cs]/Computational Geometry [cs.CG] %Z Computer Science [cs]/Numerical Analysis [cs.NA]Journal articles %X The paper answers an open problem introduced by Bezdek and Fodor (Arch. Math. 74:75-80, 2000). The width of any unit-diameter octagon is shown to be less than or equal to 1 4 10+27 √ − − − − − − − √ and there are infinitely many small octagons having this optimal width. The proof combines geometric and analytical reasoning as well as the use of a recent version of the deterministic and reliable global optimization code IBBA based on interval and affine arithmetics. The code guarantees a certified numerical accuracy of 1×10 −7 . %G English %L hal-00847250 %U https://hal.science/hal-00847250 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ INSMI %~ SMS %~ ENIB %~ LAB-STICC_ENIB %~ UT1-CAPITOLE %~ LAB-STICC %~ INSTITUTS-TELECOM %~ IRIT %~ IRIT-APO %~ IRIT-CISO %~ IRIT-INPT %~ TOULOUSE-INP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP