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On points constructible from conics. (English) Zbl 0878.51005

It is known that some geometric constructions are impossible if one uses just a straightedge and compass. What if one is allowed to use conics? It was known to the ancient Greeks that (i) duplication of the cube is possible by using a parabola (Menaechmus), (ii) trisection of an arbitrary angle is possible by using a hyperbola (Pappus), (iii) a regular heptagon can be constructed (Archimedes).

In the present paper, the author considers the problem of which points are constructible from conics. In particular, he determines which regular polygons are conic-constructible.


MSC:
51M15Geometric constructions
References:
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[2]D.J.H. Garling,A Course in Galois Theory, Cambridge University Press, Cambridge, 1986.
[3]T.L. Heath,A History of Greek Mathematics, Oxford University Press, Oxford, 1960.
[4]T.L. Heath,A Manual of Greek Mathematics, Dover Publications, New York, 1963.
[5]N. Jacobson,Basic Algebra I, W.H. Freeman & Co., New York, 1985.
[6]D. Robinson,A Course in the Theory of Groups, Springer-Verlag, New York, 1982.