N-sphereIn mathematics, an n-sphere or a hypersphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in (n + 1)-dimensional Euclidean space that are situated at a constant distance r from a fixed point, called the center. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit n-sphere or simply the n-sphere for brevity.
3-sphereIn mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. It may be embedded in 4-dimensional Euclidean space as the set of points equidistant from a fixed central point. Analogous to how the boundary of a ball in three dimensions is an ordinary sphere (or 2-sphere, a two-dimensional surface), the boundary of a ball in four dimensions is a 3-sphere (an object with three dimensions). A 3-sphere is an example of a 3-manifold and an n-sphere.
SailA sail is a tensile structure, which is made from fabric or other membrane materials, that uses wind power to propel sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and even sail-powered land vehicles. Sails may be made from a combination of woven materials—including canvas or polyester cloth, laminated membranes or bonded filaments, usually in a three- or four-sided shape. A sail provides propulsive force via a combination of lift and drag, depending on its angle of attack, its angle with respect to the apparent wind.
Riemann sphereIn mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane: the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value for infinity. With the Riemann model, the point is near to very large numbers, just as the point is near to very small numbers. The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as well-behaved.
Sail componentsSail components include the features that define a sail's shape and function, plus its constituent parts from which it is manufactured. A sail may be classified in a variety of ways, including by its orientation to the vessel (e.g. fore-and-aft) and its shape, (e.g. (a)symmetrical, triangular, quadrilateral, etc.). Sails are typically constructed out of flexible material that is shaped by various means, while in use, to offer an appropriate airfoil, according to the strength and apparent direction of the wind.
