<P> The shape of a quadrilateral is associated with two complex numbers p, q . If the quadrilateral has vertices u, v, w, x, then p = S (u, v, w) and q = S (v, w, x). Artzy proves these propositions about quadrilateral shapes: </P> <Ol> <Li> If p = (1 − q) − 1, (\ displaystyle p = (1 - q) ^ (- 1),) then the quadrilateral is a parallelogram . </Li> <Li> If a parallelogram has arg p = arg q, then it is a rhombus . </Li> <Li> When p = 1 + i and q = (1 + i) / 2, then the quadrilateral is square . </Li> <Li> If p = r (1 − q − 1) (\ displaystyle p = r (1 - q ^ (- 1))) and sgn r = sgn (Im p), then the quadrilateral is a trapezoid . </Li> </Ol> <Li> If p = (1 − q) − 1, (\ displaystyle p = (1 - q) ^ (- 1),) then the quadrilateral is a parallelogram . </Li> <Li> If a parallelogram has arg p = arg q, then it is a rhombus . </Li>

Objects put together in a group based on common criteria such as color or shape are called