Crofton formulas and convexity condition for secantoptics
Mozgawa, Witold ; Skrzypiec, Magdalena
Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, p. 435-445 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The aim of this paper is to study some properties of secantoptics, defined in [8]. We show that any evolutoid of a given oval $C$ is a hedgehog and that any secantoptic of an oval $C$, is an isoptic of a pair of required evolutoids. We prove some Crofton-type formulas for secantoptics and give a necessary and sufficient condition for a secantoptic to be convex.
Published online : 2009-08-15
Classification:  secantoptic,  isoptic,  secant,  hedgehog,  evolutoid,  53A04,  53C44 
@article{1251832370,
     author = {Mozgawa, Witold and Skrzypiec, Magdalena},
     title = {Crofton formulas and convexity condition for secantoptics},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 435-445},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251832370}
}

Mozgawa, Witold; Skrzypiec, Magdalena. Crofton formulas and convexity condition for secantoptics. Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, pp.  435-445. http://gdmltest.u-ga.fr/item/1251832370/