Original Research

Equipartitioning and balancing points of polygons

Shunmugam Pillay, Poobhalan Pillay
Pythagoras | Issue 71 | a2 | DOI: https://doi.org/10.4102/pythagoras.v0i71.2 | © 2010 Shunmugam Pillay, Poobhalan Pillay | This work is licensed under CC Attribution 4.0
Submitted: 04 July 2010 | Published: 04 July 2010

About the author(s)

Shunmugam Pillay, School of Mathematical Sciences, University of KwaZulu‐Natal, South Africa
Poobhalan Pillay, School of Mathematical Sciences, University of KwaZulu‐Natal, South Africa

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Abstract

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

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