This paper presents research into closed orbits parallel to quadrilaterals inscribed in various geometric shapes that can be represented by mathematical functions: straight lines, circles, ellipses, parabolas, and hyperbolas. Mathematical proofs have been given for the existence of an infinite number of parallel orbits for each of these shapes. Quadrilaterals parallel to a quadrilateral inscribed in a circle were found to have two interesting characteristics. The mathematics was conducted with student mathematics teachers and teacher trainees, accompanied by dynamic research using computer software.