Neusis constructions - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T10:25:32Z http://mathoverflow.net/feeds/question/31944 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/31944/neusis-constructions Neusis constructions Ricky Demer 2010-07-15T02:55:14Z 2013-04-25T20:47:22Z <p>Is there some simple description of which complex numbers are "constructible" with straightedge and compass and neusis?</p> <p>See <a href="http://en.wikipedia.org/wiki/Constructible_number" rel="nofollow">http://en.wikipedia.org/wiki/Constructible_number</a> and <a href="http://en.wikipedia.org/wiki/Neusis" rel="nofollow">http://en.wikipedia.org/wiki/Neusis</a>.</p> http://mathoverflow.net/questions/31944/neusis-constructions/31951#31951 Answer by John Stillwell for Neusis constructions John Stillwell 2010-07-15T03:41:51Z 2010-07-15T03:41:51Z <p>Just as straightedge and compass constructions give the numbers in the closure of the rationals under square roots, neusis gives the closure of the rationals under square roots <em>and</em> cube roots.</p> <p>For more details, also for an alternate characterization in terms of origami, see <a href="http://www.math.sjsu.edu/~alperin/TRFin.pdf" rel="nofollow">this paper</a> by Roger Alperin.</p> http://mathoverflow.net/questions/31944/neusis-constructions/31962#31962 Answer by Gerry Myerson for Neusis constructions Gerry Myerson 2010-07-15T05:14:12Z 2010-07-15T05:14:12Z <p>I don't know whether this amounts to the same thing as a neusis, but there's an article by Arthur Baragar, Constructions using a compass and twice-notched straightedge, Amer. Math. Monthly 109 (2002), no. 2, 151-164, MR 2003d:51015, which might possibly be of some use. </p>