antipodal points

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antipodal points

[an¦tip·əd·əl ′pȯins]
(mathematics)
The points at opposite ends of a diameter of a sphere.
References in periodicals archive ?
Place the initial point [[PHI].sub.b=0] = [[PHI].sub.0] and its antipodal point [[bar.[PHI]].sub.b=0] [[PHI].sub.B/2] into {[PHI]}.
If [[PHI].sub.[beta]] is placed into {[PHI]}, then its antipodal point [bar.[PHI].sub.[beta]] is also placed into {[PHI]}.
[F.sub.2] determines uniquely its antipodal point [F'.sub.2] and the referring spherical straight line f which is the great circle at spherical distance 0,5[pi] from both points [F.sub.2] and [F'.sub.2].
Plane elliptic geometry is closely related to spherical geometry, but it differs in that antipodal points on the sphere are identified.
On the other hand, Borsuk's theorem only requires the mapping f to be continuous on the ball and to fulfill a non-colinearity condition for the function values at all pairs of antipodal points on the boundary of the ball.
The first strict circumnavigation, covering two antipodal points, was made by Lowell Smith and Leslie Arnold in two US Army Douglas DWC seaplanes in 57 legs beginning and ending in Chicago in 1924
The Guinness book of world record rules require competitors to travel at least 18,000 miles by land and 8,000 by sea or air, via two antipodal points.
Each cone intersects the unit sphere in one of six ways: an empty intersection, a single point, a pair of antipodal points, an arc of a great circle, a great circle, or the entire sphere.
Mr Springbett, aged 61, and Brother Michael, 59 - a member of the Order of the Good Shepherd - chose Madrid Airport and Ti Tree Point on Highway 52 in the south-east corner of New Zealand's northern island as their antipodal points.

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