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.…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…