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In geography, the antipode (/ ˈ æ n t ɪ ˌ p oʊ d, æ n ˈ t ɪ p ə d i /) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal (/ æ n ˈ t ɪ p ə d əl /) to each other are situated such that a straight line connecting the two would pass through Earth's center.
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).
An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.
The converse is also true: it is possible to prove Tucker's lemma from the Borsuk–Ulam theorem. Therefore, these two theorems are equivalent. There are several fixed-point theorems which come in three equivalent variants: an algebraic topology variant, a combinatorial variant and a set-covering variant. Each variant can be proved separately ...
The points at right angles to the North and South points are the East and West points. Going around the disk clockwise from the North point, one encounters in order the West point, the South point, and then the East point. This is opposite to the order on a terrestrial map because one is looking up instead of down.
Port: the left side of the ship, when facing forward (opposite of "starboard"). [1] Starboard: the right side of the ship, when facing forward (opposite of "port"). [1] Stern: the rear of a ship (opposite of "bow"). [1] Topside: the top portion of the outer surface of a ship on each side above the waterline. [1] Underdeck: a lower deck of a ...
The two line segments connecting opposite points of tangency have equal length. The tangent lengths, distances from a point of tangency to an adjacent vertex of the quadrilateral, are equal at two opposite vertices of the quadrilateral. (At each vertex, there are two adjacent points of tangency, but they are the same distance as each other from ...
The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector. The proof of the correctness of this construction is fairly intuitive, relying on the symmetry of the problem.