Search results
Results from the WOW.Com Content Network
All of the curves are circles: the curves that intersect 0,0,0,1 have an infinite radius (= straight line). In mathematics , an n -sphere or hypersphere is an n {\displaystyle n} - dimensional generalization of the 1 {\displaystyle 1} -dimensional circle and 2 {\displaystyle 2} -dimensional sphere to any non-negative ...
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
For any natural number n, an n-sphere, often denoted S n, is the set of points in (n + 1)-dimensional Euclidean space that are at a fixed distance r from a central point of that space, where r is, as before, a positive real number. In particular: S 0: a 0-sphere consists of two discrete points, −r and r; S 1: a 1-sphere is a ...
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
where is the area (of any shape) on the surface of the sphere and is the radius of the sphere. Solid angles are often used in astronomy, physics, and in particular astrophysics. The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance.
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
Specifically: A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every open cover of the space has a refinement that is a cover by disjoint open sets.
The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states. [3] [4] The Bloch sphere may be generalized to an n-level quantum system, but then the visualization is less useful. The natural metric on the Bloch sphere is the Fubini–Study metric.