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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