Crofton formulas and convexity condition for secantoptics
Witold Mozgawa and Magdalena Skrzypiec
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 16, Number 3 (2009), 435-445.
Abstract
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.
Primary Subjects: 53A04, 53C44
Keywords: secantoptic; isoptic; secant; hedgehog; evolutoid
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bbms/1251832370
Zentralblatt MATH identifier:
05612289
Bulletin of the Belgian Mathematical Society - Simon Stevin
