Equidissections of kite-shaped quadrilaterals

Jepsen, Charles; Sedberry, Trevor; Hoyer, Rolf

doi:10.2140/involve.2009.2.89

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Equidissections of kite-shaped quadrilaterals

Charles H. Jepsen, Trevor Sedberry and Rolf Hoyer

Vol. 2 (2009), No. 1, 89–93

DOI: 10.2140/involve.2009.2.89

Abstract

Let $Q (a)$ be the convex kite-shaped quadrilateral with vertices $(0, 0)$ , $(1, 0)$ , $(0, 1)$ , and $(a, a)$ , where $a > 1 ∕ 2$ . 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

Vol. 2, No. 1, 2009