Involutes of polygons of constant width in Minkowski planes
Craizer, Marcos ; Martini, Horst, 1954-
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 ▫$P$▫.
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