Quadrangles Inscribed in a Closed Curve and the Vertices of a Curve |
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Authors: | V V Makeev |
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Institution: | (1) St. Petersburg State University, St. Petersburg, Russia |
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Abstract: | Let ABCDE be a pentagon inscribed in a circle. It is proved that if
is a C4-generic smooth convex planar oval with four vertices (stationary points of curvature), then there are two similarities φ
such that the quadrangle φ(ABCD) is inscribed in
and the point φ(E)lies inside
, as well as two similarities ψ such that the quadrangle ψ(ABCD) is inscribed in
and ψ(E)lies outside
. Itisalsoprovedthatif n is odd, then any smoothly embedded circle γ ↪ ℝn contains the vertices of an equilateral (n + 1)-link polygonal line lying in a hyperplane of ℝn. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 241–251. |
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Keywords: | |
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