Minimum-Area ellipse containing a finite set of points. I

  • Yu. I. Petunin
  • В. V. Rublev

Abstract

From the geometric point of view, we consider the problem of construction of a minimum-area ellipse containing a given convex polygon. For an arbitrary triangle, we obtain an equation for the boundary of the minimum-area ellipse in explicit form. For a quadrangle, the problem of construction of a minimumarea ellipse is connected with the solution of a cubic equation. For an arbitrary polygon, we prove that if the boundary of the minimum-area ellipse has exactly three common points with the polygon, then this ellipse is the minimum-area ellipse for the triangle obtained.
Published
25.07.1998
How to Cite
PetuninY. I., and RublevВ. V. “Minimum-Area Ellipse Containing a Finite Set of Points. I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 50, no. 7, July 1998, pp. 980–988, https://umj.imath.kiev.ua/index.php/umj/article/view/4877.
Section
Research articles