```Date: May 28, 2002 1:04 PM
Author: Michael Lambrou
Subject: RE: Angle Trisection

> > Here are few examples of angles that can be triseced, but this is not> obvious:> > 1. Pi/7 can be trisected since Pi/21 = Pi/3 - 2*Pi/7Dear Sergei, Thank you for the interesting comments on angles that can be trisected. There is, however, a problem with the statement I isolated above, and the argument is not correct. To see why, let me give a more transparentexample.It is like saying, for example, that an angle of 10 degrees can beconstructed because 10 = 30 - 2.10.  On the other hand we know that an angle of 10 degrees cannot beconstructed (If it could, so would its double 20, so 60 could betrisected. But it is well known that it cannot). To return to the above, it only says: IF (this is a big "if" here) youcould construct Pi/7, then you could trisect it. The problem is that youcannot construct Pi/7. If you could, then doubling it would give you thecentral angle of a regular septagon. But it is well known that theregular septagon cannot be constucted using ruler and compass. (Incidently, for the benefit of those who like some history of maths,this particular regular polygon was constructed by Archimedes using atype of neusis construction. The original Greek text is lost, but thereis an Arabic translation of it. I highly recommend that you find a textthat has an English translation of it. "The Works of Archimedes" by T.Heath is one such.) All the best,Michael Lambrou.
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