Sphere

A sphere (from Ancient Greek σφαῖρα (sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and the distance r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings. Although the figure of Earth is not perfectly spherical, terms borrowed from geography are convenient to apply to the sphere. A particular line passing through its center defines an axis (as in Earth's axis of rotation ). The sphere-axis intersection defines two antipodal poles ( north pole and south pole ). The great circle equidistant to the poles is called the equator . Great circles through the poles are called lines of longitude or meridians . Small circles on the sphere that are parallel to the equator are circles of latitude (or parallels ). In geometry unrelated to astronomical bodies, geocentric terminology should be used only for illustration and noted as such, unless there is no chance of misunderstanding.