QUADRANGLES INSCRIBED IN A CLOSED CURVE AND THE VERTICES OF A CURVE


    loading  Checking for direct PDF access through Ovid

Abstract

Let ABCDE be a pentagon inscribed in a circle. It is proved that if 𝒪 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 𝒪 and the point Φ(E)lies inside 𝒪, as well as two similarities ψ such that the quadrangle ψ(ABCD) is inscribed in 𝒪 and ψ(E)lies outside 𝒪. 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.

    loading  Loading Related Articles