sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the "radius" of the sphere. The maximum straight distance through the sphere is known as the "diameter" of the sphere. It passes through the center and is thus twice the radius. In mathematics, a careful distinction is made between the sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior). In 3 dimensions, the volume inside a sphere (that is, the volume of a ball) is given by the formula where r is the radius of the sphere and π is the constant pi. This formula was first derived by Archimedes, who showed that the...