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In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a ''point at infinity''. The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point (there is no "parallel" case). There are many equivalent ways to formally define a projective line; one of the most common is to define a projective line over a field ''K'', commonly denoted P1(''K''), as the set of one-dimensional subspaces of a two-dimensional ''K''-vector space. This definition is a special instance of the general definition of a projective space. ==Homogeneous coordinates== An arbitrary point in the projective line P1(''K'') may be represented by an equivalence class of ''homogeneous coordinates'', which take the form of a pair : of elements of ''K'' that are not both zero. Two such pairs are equivalent if they differ by an overall nonzero factor ''λ'': : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「projective line」の詳細全文を読む スポンサード リンク
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