“Pascal's theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Pascal's theorem

释义

Pascal's theorem

(Pascal's mystic hexagram) A theorem of projective geometry: given two triples of points A,B,C and A′,B′,C′ on a non-degenerate conic, the points of intersection

are collinear. Pappus' Hexagon Theorem can be seen as a version of Pascal's theorem for degenerate conics.

Pascal's ‘mystic hexagram'

The dual of Pascal's theorem is Brianchon's theorem: if a hexagon with vertices P1, P2, P3, P4, P5, P6 circumscribes a non-degenerate conic, then the hexagon's diagonals P1P4, P2P5, P3P6 are concurrent. See duality.

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