Pizza Again? On the Division of Polygons into Sections with a Common Origin

Autor/inn/en	Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina
Titel	Pizza Again? On the Division of Polygons into Sections with a Common Origin
Quelle	In: International Journal of Mathematical Education in Science and Technology, 49 (2018) 2, S.281-293 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2017.1383525
Schlagwörter	Geometric Concepts; Plane Geometry; Arithmetic; Mathematics Instruction; Secondary School Mathematics + Suchen Sie Ihr Suchwort? Elementare Geometrie; Planimetrie; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht
Abstract	The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to divide a regular polygon into any number of equal-area pieces using line segments originating from the centre. Moreover, it turns out that there are infinite ways to do the division. Discovering the basic invariant involved allows application of the same procedure to divide any tangential polygon, as after suitable adjustment, it can be used also for rectangles and parallelograms. Further generalization offers many additional solutions of the problem, and some of them are presented for the case of an arbitrary triangle and a square. Links to dynamic demonstrations in GeoGebra serve to illustrate the main results. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01