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 ?$P$?.

Rights

URN

URN:NBN:SI:doc-9E91HJN7

COBISSID

17842009

Added

29.05.2020

Metadata

Citation

APA:

Craizer, Marcos, Martini, Horst (2016). Involutes of polygons of constant width in Minkowski planes. Ars mathematica contemporanea, volume 11, issue 1, str. 107-125. URN:NBN:SI:doc-9E91HJN7 from http://www.dlib.si

MLA:

Craizer, Marcos, Martini, Horst. "Involutes of polygons of constant width in Minkowski planes." Ars mathematica contemporanea volume 11. issue 1 (2016) str. 107-125.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-9E91HJN7>

Ars mathematica contemporanea
2008-
(Assembly record)