Deviation of the centroid of a convex figure from the center of the circumscribed disk

1976 ◽  
Vol 19 (2) ◽  
pp. 97-99
Author(s):  
Yu. G. Dutkevich
Keyword(s):  
Convex Figure

On the approximation of convex, closed plane curves by multifocal ellipses

1982 ◽  
Vol 19 (A) ◽  
pp. 89-96
Author(s):  
P. Erdös I. Vincze
Keyword(s):  
Open Problem ◽  
Closed Curve ◽  
Plane Curves ◽  
Straight Segment ◽  
Convex Figure ◽  
Closed Plane

The question whether a convex closed curve can be approximated by ellipses having a large number of foci is considered. It is shown that the limiting, convex figure of multifocal ellipses may have only one single straight segment. This happens only in the case, when the foci tend partly to infinity and partly to points of the line through the straight segment. The approximations of certain ‘distance integrals' are treated; the characterization of approximability remains an open problem.

On the approximation of convex, closed plane curves by multifocal ellipses

1982 ◽  
Vol 19 (A) ◽  
pp. 89-96 ◽  
Author(s):  
P. Erdös I. Vincze
Keyword(s):  
Open Problem ◽  
Closed Curve ◽  
Plane Curves ◽  
Straight Segment ◽  
Convex Figure ◽  
Closed Plane

The question whether a convex closed curve can be approximated by ellipses having a large number of foci is considered. It is shown that the limiting, convex figure of multifocal ellipses may have only one single straight segment. This happens only in the case, when the foci tend partly to infinity and partly to points of the line through the straight segment. The approximations of certain ‘distance integrals' are treated; the characterization of approximability remains an open problem.

Polygons Inscribed in a Convex Figure

2016 ◽  
Vol 212 (5) ◽  
pp. 527-530
Author(s):  
V. V. Makeev
Keyword(s):  
Convex Figure
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