[¦par·ə¦bäl·ik si¦lin·drə·kəl kō′ȯrd·ən·ət ‚sis·təm] (mathematics) A three-dimensional coordinate system in which two of the coordinates depend on the x and y coordinates in the same manner as parabolic coordinates and are independent of the z coordinate, while the third coordinate is directly proportional to the z coordinate.