Closed orbits parallel to quadrilaterals inscribed in various conic sections

摘要

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.