Pascal's theorem

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.

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 Möbius in 1847, as follows: suppose a polygon with sides is inscribed in a conic section, and opposite pairs of sides are extended until they meet in points. Then if of those points lie on a common line, the last point will be on that line, too.

See also

• Projective geometry

External links

• Interactive demo of Pascal's theorem (requires a Java-enabled browser)
• Another one