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单词 Desargues Theorem
释义

Desargues Theorem

中文百科

笛沙格定理 Desargues's theorem

(重定向自Desargues Theorem)
Perspective triangles. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second.

笛沙格(Desargues)定理说明:在射影空间中,有六点A,B,C,a,b,c。Aa,Bb,Cc共点若且唯若AB∩ab,BC∩bc,CA∩ca共线。

在射影几何的对偶性来看,笛沙格定理是自对偶的。

英语百科

Desargues's theorem 笛沙格定理

(重定向自Desargues Theorem)
Perspective triangles. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second.
The Desargues configuration viewed as a pair of mutually inscribed pentagons: each pentagon vertex lies on the line through one of the sides of the other pentagon.

In projective geometry, Desargues's theorem, named after Girard Desargues, states:

Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C. Axial perspectivity means that lines ab and AB meet in a point, lines ac and AC meet in a second point, and lines bc and BC meet in a third point, and that these three points all lie on a common line called the axis of perspectivity. Central perspectivity means that the three lines Aa, Bb and Cc are concurrent, at a point called the center of perspectivity.

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更新时间:2025/6/17 20:48:24