Abstract
We investigate equidissections of a trapezoid
T
(
a
)
, where the ratio of the lengths of two parallel sides is
a
. (An
equidissection is a dissection into triangles of equal areas.) An integer
n
is in the
spectrum
S
(
T
(
a
)
)
if
T
(
a
)
admits an equidissection into
n
triangles. Suppose
a
is algebraic of degree 2 or 3, with each conjugate over
Q
having positive real part. We show that if
n
is large enough,
n
is in
S
(
T
(
a
)
)
iff
n
/
(
1
+
a
)
is an algebraic integer. If, in addition,
a
is the larger root of a monic quadratic polynomial with integer coefficients, we give a complete description of
S
(
T
(
a
)
)
.