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Is there some simple description of which complex numbers are "constructible" with straightedge and compass and neusis?

See http://en.wikipedia.org/wiki/Constructible_number and http://en.wikipedia.org/wiki/Neusis.

edited Apr 25 at 20:47

ε-δ
1,028●5●16

asked Jul 15 2010 at 2:55

Ricky Demer
6,401●8●31

John Stillwell · Accepted Answer · 2010-07-15 03:41:51Z UTC

7

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 and cube roots.

For more details, also for an alternate characterization in terms of origami, see this paper by Roger Alperin.

answered Jul 15 2010 at 3:41

John Stillwell
8,121●5●41●79

	This would seem to be the same as the set of "conic-constructible" numbers, as per Videla, On points constructible from conics, Math Intelligencer 19 (1997) 53-57. – Gerry Myerson Jul 16 2010 at 1:14
	Gerry, yes it is. In fact, Alperin cites this paper. – John Stillwell Jul 16 2010 at 1:46

Gerry Myerson · Answer 2 · 2010-07-15 05:14:12Z UTC

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.

Neusis constructions

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