Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%.
Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%. The Banach-Tarski paradox states that a solid one of these objects can be cut into finitely many pieces and re-assembled into two copies of the same size as the original. For a  non-Euclidean geometry occurring on these objects, triangles have angle sum greater than 180 degrees. (*) Archimedes derived the formula for the volume of this figure by noting that it occupied two-thirds of the volume of its circumscribed cylinder. This figure has surface area equal to four pi times the radius squared, and volume four-thirds pi times radius cubed. For ten points, name this three-dimensional analogue of a circle, the outer surface of a ball.
Kepler's Conjecture postulates that these objects can be packed with a density of approximately 74%.
{sphere} (accept {ball} before mentioned)