A generalized Winternitz Theorem

Prosenjit Bose; Paz Carmi; Ferran Hurtado; Pat Morin

doi:10.1007/s00022-011-0076-0

A generalized Winternitz Theorem

Prosenjit Bose
, Paz Carmi
, Ferran Hurtado
, Pat Morin

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.

Original language	English
Pages (from-to)	29-35
Number of pages	7
Journal	Journal of Geometry
Volume	100
Issue number	1-2
DOIs	https://doi.org/10.1007/s00022-011-0076-0
State	Published - 1 Apr 2011

Keywords

Centerpoint Theorem
Polygons
Winternitz' Theorem

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-011-0076-0

Cite this

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title = "A generalized Winternitz Theorem",

abstract = "We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.",

keywords = "Centerpoint Theorem, Polygons, Winternitz' Theorem",

author = "Prosenjit Bose and Paz Carmi and Ferran Hurtado and Pat Morin",

year = "2011",

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doi = "10.1007/s00022-011-0076-0",

language = "English",

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T1 - A generalized Winternitz Theorem

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Hurtado, Ferran

AU - Morin, Pat

PY - 2011/4/1

Y1 - 2011/4/1

N2 - We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.

AB - We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.

KW - Centerpoint Theorem

KW - Polygons

KW - Winternitz' Theorem

UR - https://www.scopus.com/pages/publications/80255137577

U2 - 10.1007/s00022-011-0076-0

DO - 10.1007/s00022-011-0076-0

M3 - Article

AN - SCOPUS:80255137577

SN - 0047-2468

VL - 100

SP - 29

EP - 35

JO - Journal of Geometry

JF - Journal of Geometry

IS - 1-2

ER -

A generalized Winternitz Theorem

Abstract

Keywords

ASJC Scopus subject areas

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