```Date: Jul 22, 2002 9:17 PM
Author: Rouben Rostamian
Subject: Re: Trisection

Steve Gray <stevebg@adelphia.net> wrote:> There is an article in the Monthly comparing about 8> methods for approximate trisection. It includes the number> of steps each one needs and the errors they give. See> The American Mathematical Monthly, May 1954, page 334,> by Jamison.  I have not examined Mark's method relative to> any of those.  Someone might consider writing an updated> version. But not me; I'm into constructions on N-gons> for now.I looked up that article.  It is short and insightful.  It alsoinspired me to do a thorough error analysis of the the trisectionalgorithm proposed by Mark Stark in this thread; see:     http://mathforum.org/epigone/geometry-puzzles/quumeldplyr/74tzzy089efg@legacyIt turns out that Mark's construction is amenable to a prettynice analysis and a precise expression can be obtained forthe error.  In his notation, if we let the measure of the angleAOB be T and the measure of the angle AOE be a, then the errore(T,a) is given by the expression:    e(T,a) = T/6 - a/2 - arcsin((1/3)sin(T/2 - 3a/2)).I have placed the derivation on my web site.  The statement ofthe problem is in    http://www.math.umbc.edu/~rouben/Geometry/trisect-stark.htmland the proof in:    http://www.math.umbc.edu/~rouben/Geometry/trisect-stark-proof.htmlIt turns out that the accuracy of Mark's construction sort of falls between the two methods described in the Monthlyarticle mentioned by Steve.  Definitive comparison is difficult because Mark's method involves an arbirarychoice, while Jamison's doesn't.  I am basing thecomparison statement made above by setting a=T/4 incalculating the error e(T,a).--Rouben Rostamian <rostamian@umbc.edu>
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