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Limiting parallel
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Limiting parallel : ウィキペディア英語版
Limiting parallel

In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line l through a point P not on line R; however, in the plane, two parallels may be closer to l than all others (one in each direction of R).
Thus it is useful to make a new definition concerning parallels in neutral geometry. If there are closest parallels to a given line they are known as the limiting parallel, asymptotic parallel or horoparallel (horo from (ギリシア語:ὅριον ) — border).
For rays, the relation of limiting parallel is an equivalence relation, which includes the equivalence relation of being coterminal.
Limiting parallels may form two, or three sides of a limit triangle.
==Definition==

A rays Aa is a limiting parallel to a ray Bb if they are coterminal or if they lie on distinct lines not equal to the line AB, they do not meet, and every ray in the interior of the angle BAa meets the ray Bb.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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