Author： Makeev V.
Publisher： Springer Publishing Company
ISSN： 1072-3374
Source： Journal of Mathematical Sciences, Vol.100, Iss.3, 2000-06, pp. : 2303-2306
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Abstract
Two theorems are proved. Let the points A1, A2, A3, A4, and A5 be the vertices of a convex pentagon inscribed in an ellipse, let Κ⊂ℜ2 be a convex figure, and let A0 be a fixed distinguished point of its boundary ϖK. If the sum of any two of the neighboring angles of the pentagon A1A2A3A4A5 is greater than π or the boundary ϖK is C4-smooth and has positive curvature, then some affine image of the pentagon A1A2A3A4A5 is inscribed in K and has A0 as the image of the vertex A1. (This is not true for arbitrary pentagons incribed in an ellipse and for arbitrary convex figures.) Bibliography: 4 titles.
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