Pascal's theorem states that if an arbitrary hexagon is inscribed in any conic section, and opposite pairs of sides are extended until they meet, the three intersection points will lie on a straight line, the Pascal line of that configuration. In the Euclidean plane, the theorem has exceptions; its natural home is the projective plane.

This theorem is a generalization of Pappus's hexagon theorem, and the projective dual of Brianchon's theorem. It was discovered by Blaise Pascal when he was only 16 years old.

The theorem was generalized by M�bius in 1847, as follows: suppose a polygon with 4n + 2 sides is inscribed in a conic section, and opposite pairs of sides are extended until they meet in 2n + 1 points. Then if 2n of those points lie on a common line, the last point will be on that line, too.

External links

• Interactive demo of Pascal's theorem (http://www.cut-the-knot.org/Curriculum/Geometry/Pascal.shtml) (requires a Java-enabled browser)
• 60 Pascal Lines (http://www.cut-the-knot.org/Curriculum/Geometry/PascalLines.shtml) (requires a Java-enabled browser)
• Another one (http://www.jimloy.com/cindy/pascal.htm)

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