points on a sphere or angles in a circle are measured in units called
radians
title: Radian text: Radian The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at ). The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and the radian is now considered an SI derived unit. Separately, the SI unit of solid angle measurement is the steradian. The radian is most title: Sphere text: -sphere of unit radius centered at the origin is denoted and is often referred to as "the" -sphere. Note that the ordinary sphere is a 2-sphere, because it is a 2-dimensional surface (which is embedded in 3-dimensional space). The surface area of the unit ()-sphere is where is Euler's gamma function. Another expression for the surface area is and the volume is the surface area times or General recursive formulas also exist for the volume of an -ball. More generally, in a metric space , the sphere of center and radius is the set of points such that . If title: Angular unit text: the angle is measured as long as each angle is measured in the same unit. One "radian" is the angle subtended by an arc of a circle that has the same length as the circle's radius. The radian is the derived quantity of angular measurement in the SI system. By definition, it is dimensionless, though it may be specified as "rad" to avoid ambiguity. Angles measured in degrees, are shown with the symbol °. Subdivisions of the degree are minute (symbol ', 1' = 1/60°) and second {symbol ", 1" = 1/3600°}. An angle of 360° corresponds to the angle title: Sphere text: space with possible self-intersections but without creating any crease, in a process called sphere eversion. The basic elements of Euclidean plane geometry are points and lines. On the sphere, points are defined in the usual sense. The analogue of the "line" is the geodesic, which is a great circle; the defining characteristic of a great circle is that the plane containing all its points also passes through the center of the sphere. Measuring by arc length shows that the shortest path between two points lying on the sphere is the shorter segment of the great circle that includes the points. title: Sphere text: Sphere A sphere (from Greek σφαῖρα — "sphaira", "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk"). Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance from a given point, but in a three-dimensional space. This distance is the radius of the ball, which is made up from all points with a distance less than from the given point,