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Self-Intersection Points of Generalized Koch Curves

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Title: Self-Intersection Points of Generalized Koch Curves
Author(s): Cantrell, Michael; Palagallo, Judith
Subject(s): curve self-similar curve simple curve self-intersecting curve
Abstract: We present a two-parameter family of curves Ka,ө that are modifications of the Koch curve. For each ө, there is a corresponding pivotal value a(ө) of a, where Ka,ө is simple if a > a(ө), and Ka,ө is self-intersecting if a < a(ө). We find a(ө), for ө € (0, π/3], then show that the pivotal-valued curves comprise two classes of self-intersecting curves that we characterize by whether or not ө= π/n for some even positive integer n > 2.
Issue Date: 2011-06
Publisher: World Scientific Publishing
Citation Info: Cantrell, M. & Palagallo, J. 2011. Self-Intersection Points of Generalized Koch Curves. Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 19(2): 213-220. DOI: 10.1142/S0218348X11005257
Type: Article
Description: Electronic version of an article published as Fractals, 19, 2, 2011, 213-220. DOI: 10.1142/S0218348X11005257 © copyright World Scientific Publishing Company http://www.worldscinet.com/fractals/fractals.shtml
URI: http://hdl.handle.net/10027/8144
ISSN: 0218-348X
Sponsor: Research supported by NSF-REU grant DMS-0354022 at The University of Akron.
Date Available in INDIGO: 2012-03-01
 

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