Vol. 2, No. 1, 2009

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Equidissections of kite-shaped quadrilaterals

Charles H. Jepsen, Trevor Sedberry and Rolf Hoyer

Vol. 2 (2009), No. 1, 89–93
Abstract

Let Q(a) be the convex kite-shaped quadrilateral with vertices (0,0), (1,0), (0,1), and (a,a), where a > 12. We wish to dissect Q(a) into triangles of equal areas. What numbers of triangles are possible? Since Q(a) is symmetric about the line y = x,  Q(a) admits such a dissection into any even number of triangles. In this article, we prove four results describing Q(a) that can be dissected into certain odd numbers of triangles.

Keywords
equidissection, spectrum
Mathematical Subject Classification 2000
Primary: 52B45
Milestones
Received: 10 June 2007
Accepted: 2 June 2008
Published: 18 March 2009

Communicated by Kenneth S. Berenhaut
Authors
Charles H. Jepsen
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States
Trevor Sedberry
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States
Rolf Hoyer
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States