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Then-point and six-partite point of a convex polygon

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
32
Identifiers
DOI: 10.1016/s0895-7177(00)00173-4
Keywords
  • Balance Functional
  • Constructive Convex Geometry
  • Geometric Optimization
Disciplines
  • Mathematics

Abstract

Abstract The n-point of a planar convex polygon is defined through a geometric optimization problem associated with a “balance” functional and wedge set. The balance functional provides a measure of the imbalance of the polygon induced through the wedge set and the n-point is defined as the point which minimizes the balance functional. The classical six-partite point is the point where three lines pass through and subdivide the polygon into six equal area subsets. The n-point and six-partite point are solved through enumerative search strategies and examples are used throughout to illustrate the solution techniques.

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