On the maximum area pentagon in a planar point set
نویسندگان
چکیده
A finite set of points in the plane is described as in convex position if it forms the set of vertices of a convex polygon. This work studies the ratio between the maximum area of convex heptagons with vertices in P and the area of the convex hull of P, where the planar point set P is in convex position.
منابع مشابه
On a Triangle with the Maximum Area in a Planar Point Set
For a planar point set P in general position, we study the ratio between the maximum area of an empty triangle with vertices in P and the area of the convex hull of P .
متن کاملDisjoint empty convex pentagons in planar point sets
Harborth [Elemente der Mathematik, Vol. 33 (5), 116–118, 1978] proved that every set of 10 points in the plane, no three on a line, contains an empty convex pentagon. From this it follows that the number of disjoint empty convex pentagons in any set of n points in the plane is least ⌊ n 10 ⌋. In this paper we prove that every set of 19 points in the plane, no three on a line, contains two disjo...
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We deal with only finite point sets P in the plane in general position. A point set is convex or in convex position if it determines a convex polygon. A convex subset Q of P is said to be empty if no point of P lies inside the convex hull of Q. An empty convex subset of P with k elements is also called a k-hole of P . Let P be an n planar point set in general position. For a subset Q of P , den...
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 19 شماره
صفحات -
تاریخ انتشار 2006