Salahaldeen Ibrahim Abu-Alshaikh
Jubilee School, Amman, JORDAN
In this study, closed-form volumes of hyperbolic octahedron and wide families of astroidal ellipsoids were found. Furthermore, the closed form of center of mass and mass moment of inertia for these solids were found. As a special case, the closed-form volumes of unit sphere, ellipsoids, astroidal sphere, hyperbolic octahedron and other astroidal ellipsoids were obtained exactly using a single formula that contains Gamma function. However, it is well known to the applied mathematics field that the exact volume of the hyperbolic octahedron and astroidal ellipsoids are unknown before this study. Awards won at the 2013 ISEF Second Award of $1,500 - Mathematical Sciences