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The two points P and P ' (red) are antipodal because they are ends of a diameter PP ', a segment of the axis a (purple) passing through the sphere's center O (black). P and P ' are the poles of a great circle g (green) whose points are equidistant from each (with a central right angle).
The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate. 1929 Craster parabolic =Putniņš P4: Pseudocylindrical Equal-area John Craster Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect. 1949
If the geographic coordinates (latitude and longitude) of a point on the Earth's surface are (φ, θ), then the coordinates of the antipodal point are (−φ, θ ± 180°). This relation holds true whether the Earth is approximated as a perfect sphere or as a reference ellipsoid.
As a vector line intersects the unit sphere of V in two antipodal points, projective spaces can be equivalently defined as spheres in which antipodal points are identified. A projective space of dimension 1 is a projective line , and a projective space of dimension 2 is a projective plane .
On S n, in homogeneous coordinates, (x 1, ..., x n+1), consider the subset U i with x i ≠ 0. Each U i is homeomorphic to the disjoint union of two open unit balls in R n that map to the same subset of RP n and the coordinate transition functions are smooth. This gives RP n a smooth structure.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
Lambert azimuthal equal-area projection of the world. The center is 0° N 0° E. The antipode is 0° N 180° E, near Kiribati in the Pacific Ocean.That point is represented by the entire circular boundary of the map, and the ocean around that point appears along the entire boundary.
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are