#### Vol. 2, No. 1, 2009

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### Charles H. Jepsen, Trevor Sedberry and Rolf Hoyer

Vol. 2 (2009), No. 1, 89–93
##### Abstract

Let $Q\left(a\right)$ be the convex kite-shaped quadrilateral with vertices $\left(0,0\right)$, $\left(1,0\right)$, $\left(0,1\right)$, and $\left(a,a\right)$, where $a>1∕2$. We wish to dissect $Q\left(a\right)$ into triangles of equal areas. What numbers of triangles are possible? Since $Q\left(a\right)$ is symmetric about the line $y=x$,  $Q\left(a\right)$ admits such a dissection into any even number of triangles. In this article, we prove four results describing $Q\left(a\right)$ that can be dissected into certain odd numbers of triangles.

##### Keywords
equidissection, spectrum
Primary: 52B45