Geometry of the sphere

The geometry of a sphere involves the study of its properties, such as its surface, distances, and angles, all on a perfectly round, three-dimensional shape. Every point on a sphere's surface is equidistant from its center, defining its radius. The surface area and volume can be calculated using specific formulas involving the radius. Unlike flat shapes, the sphere’s surface curves uniformly in all directions, meaning concepts like straight lines are replaced by shortest paths called geodesics, which are great circles. Understanding sphere geometry is fundamental in fields like astronomy, navigation, and physics.