Crofton-type integral formulas for star domain
type: Item
instance of: scholarly article
title: Crofton-type integral formulas for star domain
zbMATH Open document ID: 0664.53035
DOI: 10.1007/BF00182397
author: Waldemar Cieślak
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: Let C be a star-shaped curve in the Euclidean plane, i.e. let C be simply closed and bounding a domain D, star-shaped with respect to a point 0. First a special representation of differentiable star-shaped curves is introduced. Then the following extremal problem for star-shaped curves is treated: Find a straight line through 0 dividing D into extremal parts with respect to the area. Finally some simple Crofton-type integral formulas concerning straight lines through 0 and expressing e.g. the length of C and the area of D are derived.
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 4086476
zbMATH Keywords: star-shaped curve
zbMATH Keywords: extremal problem
zbMATH Keywords: area
zbMATH Keywords: Crofton-type integral formulas
reviewed by: Eberhard Teufel
MaRDI profile type: Publication
cites work: The rosettes.
description: scientific article; zbMATH DE number 4086476