Line at infinity (original) (raw)
In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line.
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| dbo:abstract | In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line. (en) Dans le plan projectif, il est possible de définir un plan affine en choisissant une droite projective quelconque, que l'on appelle alors droite à l'infini associée à ce plan affine. Deux droites affines strictement parallèles correspondent à deux droites projectives qui s'intersectent en un point situé sur la droite à l'infini, dit point à l'infini. Réciproquement, il est toujours possible de compléter un plan affine par une droite à l'infini de façon à obtenir un plan projectif, dit complété projectif de ce plan affine. Les points de cette droite correspondent exactement aux directions de droites affines. (fr) De oneindig verre rechte, oneigenlijke rechte of rechte op oneindig is de verzameling van alle punten die aan het euclidische vlak moet worden toegevoegd om ervoor te zorgen dat elke twee niet samenvallende rechte lijnen elkaar in precies één punt snijden. Met de oneindig verre rechte wordt het euclidische vlak uitgebreid tot een projectief vlak. Bij elke richting van evenwijdige lijnen hoort een punt op de oneindig verre rechte. De punten op die rechte worden oneigenlijke punten (soms ook oneindige punten) genoemd. (nl) Em geometria projetiva, a reta imprópria representa o conjunto de todas as direções de um plano, ou seja, é o conjunto de todos os seus pontos impróprios. É chamada também de reta ideal ou reta de fuga. A sua projeção no quadro de visão é conhecida como Linha do horizonte. É notado por uma letra minúscula acompanhada do símbolo do infinito r∞. O Teorema de Desargues é uma de suas demonstrações. (pt) 在幾何與拓撲學裡，無窮遠線（line at infinity）是一條附加於實（仿射）平面的，以形成一個投影平面。加上無窮遠線後，投影平面上的性質才具有封閉性，而沒有例外。無窮遠線亦被稱為理想線。 (zh) |
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| rdfs:comment | In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line. (en) De oneindig verre rechte, oneigenlijke rechte of rechte op oneindig is de verzameling van alle punten die aan het euclidische vlak moet worden toegevoegd om ervoor te zorgen dat elke twee niet samenvallende rechte lijnen elkaar in precies één punt snijden. Met de oneindig verre rechte wordt het euclidische vlak uitgebreid tot een projectief vlak. Bij elke richting van evenwijdige lijnen hoort een punt op de oneindig verre rechte. De punten op die rechte worden oneigenlijke punten (soms ook oneindige punten) genoemd. (nl) Em geometria projetiva, a reta imprópria representa o conjunto de todas as direções de um plano, ou seja, é o conjunto de todos os seus pontos impróprios. É chamada também de reta ideal ou reta de fuga. A sua projeção no quadro de visão é conhecida como Linha do horizonte. É notado por uma letra minúscula acompanhada do símbolo do infinito r∞. O Teorema de Desargues é uma de suas demonstrações. (pt) 在幾何與拓撲學裡，無窮遠線（line at infinity）是一條附加於實（仿射）平面的，以形成一個投影平面。加上無窮遠線後，投影平面上的性質才具有封閉性，而沒有例外。無窮遠線亦被稱為理想線。 (zh) Dans le plan projectif, il est possible de définir un plan affine en choisissant une droite projective quelconque, que l'on appelle alors droite à l'infini associée à ce plan affine. Deux droites affines strictement parallèles correspondent à deux droites projectives qui s'intersectent en un point situé sur la droite à l'infini, dit point à l'infini. (fr) |
| rdfs:label | Droite à l'infini (fr) Line at infinity (en) Oneindig verre rechte (nl) Reta imprópria (pt) 無窮遠線 (zh) |
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