Convergence of the shadow sequence of inscribed polygons.

Gomez Martin, Francisco and Taslakian, Perouz and Toussaint, Godfried T. (2008). Convergence of the shadow sequence of inscribed polygons.. In: "18th Fall Workshop on Computational Geometry", 31/10/2008-01/11/2008, New York, EEUU. ISBN 84-8181-227-7.

Description

Title: Convergence of the shadow sequence of inscribed polygons.
Author/s:
  • Gomez Martin, Francisco
  • Taslakian, Perouz
  • Toussaint, Godfried T.
Item Type: Presentation at Congress or Conference (Article)
Event Title: 18th Fall Workshop on Computational Geometry
Event Dates: 31/10/2008-01/11/2008
Event Location: New York, EEUU
Title of Book: Convergence of the shadow sequence of inscribed polygons.
Date: 2008
ISBN: 84-8181-227-7
Subjects:
Faculty: E.U. de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Let P be a polygon inscribed in a circle. The shadow of P is a polygon P" whose vertices are at the midpoints of the arcs of consecutive points of P. The shadow sequence P0, P1, P2, . . . is a sequence of inscribed polygons such that each Pt is the shadow ofPt−1 for all t ! 0. We show in this abstract that the shadow sequence converges to the regular polygon, and in such way that variance decreases by at least one half at every step. Our proofs extend to the more general case where instead of placing the vertices of the shadow at the ratio of 1/2 of every arc we place them at an arbitrary fixed ratio ! (0 < ! < 1)going in the clockwise or counterclockwise direction.

More information

Item ID: 4442
DC Identifier: http://oa.upm.es/4442/
OAI Identifier: oai:oa.upm.es:4442
Official URL: http://www.cs.rpi.edu/fwcg2008/
Deposited by: Memoria Investigacion
Deposited on: 01 Oct 2010 11:41
Last Modified: 20 Apr 2016 13:40
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