Pascal's theorem: Difference between revisions

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The theorem was generalized by [[August Ferdinand Möbius]] in 1847, as follows: suppose a polygon with {{math|4''n'' + 2}} sides is inscribed in a conic section, and opposite pairs of sides are extended until they meet in {{math|2''n'' + 1}} points. Then if {{math|2''n''}} of those points lie on a common line, the last point will be on that line, too.

==''Hexagrammum Mysticum''==

If six unordered points are given on a conic section, they can be connected into a hexagon in 60 different ways, resulting in 60 different instances of Pascal's theorem and 60 different Pascal lines. This [[projective configuration|configuration]] of 60 lines is called the ''Hexagrammum Mysticum''.<ref>{{harvnb|Young|1930|p=67}} with a reference to Veblen and Young, ''Projective Geometry'', vol. I, p. 138, Ex. 19.</ref><ref>{{harvnb|Conway|Ryba|2012}}</ref>