Constructing equidissections for certain classes of trapezoids Original Research Article

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