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Annulus (mathematics) Illustration of Mamikon's visual calculus method showing that the areas of two annuli with the same chord length are the same regardless of inner and outer radii. [1] In mathematics, an annulus ( pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer.
The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography. In Riemannian geometry, an exponential map is a map from a subset of a tangent space T pM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical ...
R. Radius of metric space is the infimum of radii of metric balls which contain the space completely. Radius of convexity at a point p of a Riemannian manifold is the largest radius of a ball which is a convex subset. Ray is a one side infinite geodesic which is minimizing on each interval. Riemann curvature tensor.
Unit disk. In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane ), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain ...
Earth radius (denoted as R🜨 or ) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) ( equatorial radius, denoted a) to a minimum of nearly 6,357 km (3,950 mi) ( polar radius, denoted b ).
Inversive geometry. In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties: The pencil of circles defined by A and B contains a degenerate (radius zero) circle centered at p. [1] Every circle or line that is perpendicular to both A and B passes through p.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that