337 KB33 KB200820252016Craizer, MarcosMartini, Horstštevilka:1letnik:11str. 107-125COBISSID:17842009ISSN:1855-3966URN:URN:NBN:SI:doc-9E91HJN7enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaarea evoluteBarbierov izrekBarbier's theoremcenter symmetry setcurvaturecurves of constant widthdiscrete differential geometrydiskretna diferencialna geometrijaekvidistanteequidistantsevoluta območjaevoluteevolutesgeometrija Minkowskegainvoluteinvoluteskrivulje konstantne širineMinkowski geometrymnožica središčne simetrijenormed planenormirana ravninanosilec (funkcija)support functionširina (funkcija)ukrivljenostwidth functionInvolutes of polygons of constant width in Minkowski planes|Consider a convex polygon ?$P$? in the plane, and denote by ?$U$? a homothetical copy of the vector sum of ?$P$? and ?$-P$?. Then the polygon ?$U$?, as unit ball, induces a norm such that, with respect to this norm, ?$P$? has constant Minkowskian width. We define notions like Minkowskian curvature, evolutes and involutes for polygons of constant ?$U$?-width, and we prove that many properties of the smooth case, which is already completely studied, are preserved. The iteration of involutes generates a pair of sequences of polygons of constant width with respect to the Minkowski norm and its dual norm, respectively. We prove that these sequences are converging to symmetric polygons with the same center, which can be regarded as a central point of the polygon ?$P$?Naj bo ?$P$? konveksen poligon v ravnini. Označimo z ?$U$? homotetsko kopijo vektorske vsote ?$P$? in ?$-P$?. Potem poligon ?$U$?, kot enotska krogla, inducira tako normo, da ima ?$P$? glede na to normo konstantno širino Minkowskega. Definiramo pojme kot so ukrivljenost Minkowskega, evolute in involute za poligone konstantne ?$U$?-širine, in dokažemo, da se ohranjajo mnoge lastnosti gladkega primera, ki so že popolnoma preučene. Iteracija involut generira par zaporedij poligonov konstantne širine glede na normo Minkowskega in njeno dualno normo. Dokažemo, da ta zaporedja konvergirajo k simetričnim poligonom z istim središčem, ki ga lahko obravnavamo kot središčno točko poligona ?$P$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije