WebMar 24, 2024 · On the sphere, the geodesics are great circles (like the equator). The geodesics in a space depend on the Riemannian metric , which affects the notions of distance and acceleration. Geodesics preserve a direction on a surface (Tietze 1965, pp. 26-27) and have many other interesting properties. WebIllustrated mathematics dictionary index for the letter S. Browse these definitions or use the Search function above.

Volume of a sphere - Math

A sphere (from Ancient Greek σφαῖρα (sphaîra) 'globe, ball') is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the … See more As mentioned earlier r is the sphere's radius; any line from the center to a point on the sphere is also called a radius. If a radius is extended through the center to the opposite side of the sphere, it creates a See more Spherical geometry The basic elements of Euclidean plane geometry are points and lines. On the sphere, points are defined in the usual sense. The analogue … See more Ellipsoids An ellipsoid is a sphere that has been stretched or compressed in one or more directions. More exactly, it is the image of a sphere under an affine transformation. An ellipsoid bears the same relationship to the sphere that an See more In analytic geometry, a sphere with center (x0, y0, z0) and radius r is the locus of all points (x, y, z) such that Since it can be … See more Enclosed volume In three dimensions, the volume inside a sphere (that is, the volume of a ball, but classically referred to as the volume of a sphere) is See more Circles Circles on the sphere are, like circles in the plane, made up of all points a certain distance from a … See more The geometry of the sphere was studied by the Greeks. Euclid's Elements defines the sphere in book XI, discusses various properties of the sphere in book XII, and shows how to … See more WebA line segment that connects two opposite points on the circumference of the circular base of a hemisphere and passes through its center is said to be the diameter of the hemisphere A line segment from the center of the circular base to any point on its curved surface is the radius of the hemisphere Formula for the Surface Area of a Hemisphere businesses in simsbury ct

Sphere - Definition, Formulas, Equation, Properties

WebNov 8, 2014 · (here $x^i$, $x_0^i$, $i=1, \dots, n+1$, are the coordinates of $x, x_0$ respectively), i.e. the sphere is a (hyper-)quadric or a surface of the second order of … WebA sphere (from Greek σφαίρα — sphaira, "globe, ball,") is perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two … WebDefine sphere. sphere synonyms, sphere pronunciation, sphere translation, English dictionary definition of sphere. n. 1. Mathematics A three-dimensional surface, all points of which are equidistant from a fixed point. 2. A spherical object or figure. 3. A celestial body,... businesses in silver city nm