Equipartitioning and balancing points of polygons

dc.creator	Shunmugam Pillay
dc.creator	Poobhalan Pillay
dc.date	2011-07-01T00:00:00Z
dc.date.accessioned	2015-08-12T11:22:31Z
dc.date.available	2015-08-12T11:22:31Z
dc.identifier	10.4102/pythagoras.v0i0.2
dc.identifier	1012-2346
dc.identifier	2223-7895
dc.identifier	https://doaj.org/article/8c5e044f049d4551b8338636bb8465cb
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/29424
dc.description	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.
dc.language	English
dc.publisher	AOSIS OpenJournals
dc.relation	http://www.pythagoras.org.za/index.php/pythagoras/article/view/2
dc.relation	https://doaj.org/toc/1012-2346
dc.relation	https://doaj.org/toc/2223-7895
dc.rights	CC BY
dc.source	Pythagoras, Vol 0, Iss 71, Pp 13-21 (2011)
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.title	Equipartitioning and balancing points of polygons
dc.type	article