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Convergence of the shadow sequence of inscribed polygons.
Citation
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. |
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| Author/s: |
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| 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 |
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 |
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| DC Identifier: | https://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 |
