Conic-Constructible Regular Polygons

Antreas P. Hatzipolakis xpolakis at
Tue Dec 14 21:14:58 CET 1999

Videla, Carlos R.: On points constructible from conics.
Mathematical Intelligencer 19, No.2, 53-57 (1997).
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).\par 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.
[ E.J.F.Primrose (Leicester) ]

(From Zbl)

Does anyone know which is the sequence of the R. polygons which are
conic-constructible? (since right now I have not handy the Math. Int.
volumes to check)


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