Open Access
August 2009 Crofton formulas and convexity condition for secantoptics
Witold Mozgawa, Magdalena Skrzypiec
Bull. Belg. Math. Soc. Simon Stevin 16(3): 435-445 (August 2009). DOI: 10.36045/bbms/1251832370

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.

Citation

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Witold Mozgawa. Magdalena Skrzypiec. "Crofton formulas and convexity condition for secantoptics." Bull. Belg. Math. Soc. Simon Stevin 16 (3) 435 - 445, August 2009. https://doi.org/10.36045/bbms/1251832370

Information

Published: August 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1178.53001
MathSciNet: MR2566865
Digital Object Identifier: 10.36045/bbms/1251832370

Subjects:
Primary: 53A04 , 53C44

Keywords: evolutoid , hedgehog , isoptic , secant , secantoptic

Rights: Copyright © 2009 The Belgian Mathematical Society

Vol.16 • No. 3 • August 2009
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