Polygons With Integer Sides

Combinatorial geometry is concerned with counting objects that arise in geometric settings. [2] discusses how to determine T(n), the number of in-congruent triangles with integer sides and a given perimeter n. A natural continuation of this topic is the problem of determining the number of incon-gruent quadrilaterals with integer sides and a prescribed perimeter n.Let CQ(n) denote the number of (nonrectangular) cyclic quadrilaterals with integer sides and perimeter n and TR(ri) denotes the number of such trapezoids (that are not parallelograms). [1] proves some results about CQ(n) and TR(n). Unfortunately the proof for the prerequisite of the discussion is incomplete and partly erroneous. We correct the unsuitable proof and provide a constructive proof as well. By doing so we make CQ(n) and TR(n) to be well-defined integers. Then we discuss the properties of CQ(ri) and TR(ri).