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An open ball excludes the sphere itself, while a closed ball includes the sphere: a closed ball is the union of the open ball and the sphere, and a sphere is the boundary of a (closed or open) ball. The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid.
For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is 6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles .
The homeomorphisms between an open n-ball B and R n can be classified in two classes, that can be identified with the two possible topological orientations of B. A topological n -ball need not be smooth ; if it is smooth, it need not be diffeomorphic to a Euclidean n -ball.
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.
The distance d 1 between the centers of the solution circle and C 1 is either r s + r 1 or r s − r 1, depending on whether these circles are chosen to be externally or internally tangent, respectively. Similarly, the distance d 2 between the centers of the solution circle and C 2 is either r s + r 2 or r s − r 2, again
Examples of closed surfaces include the sphere, the torus and the Klein bottle. Examples of non-closed surfaces include an open disk (which is a sphere with a puncture), a cylinder (which is a sphere with two punctures), and the Möbius strip. A surface embedded in three-dimensional space is closed if and only if it is the boundary of a solid.
An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere. Comparison between an oblate spheroid and sphere.
Perga or Perge (Hittite: Parha [a], Greek: Πέργη Perge, Turkish: Perge) was originally an ancient Lycian settlement [b] that later became a Greek city in Pamphylia. [14] It was the capital of the Roman province of Pamphylia Secunda , now located in Antalya Province on the southwestern Mediterranean coast of Turkey .