Pascal's theorem: Difference between revisions

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[[Image:Pascal'sTheoremLetteredColored.PNG|thumb|250px|Self-crossing hexagon {{math|''ABCDEF''}}, inscribed in a circle. Its sides are extended so that pairs of opposite sides intersect on Pascal's line. Each pair of extended opposite sides has its own color: one red, one yellow, one blue. Pascal's line is shown in white.]]

In [[projective geometry]], '''Pascal's theorem''' (also known as the '''hexagrammum mysticum theorem''') states that if six arbitrary points are chosen on a [[conic section|conic]] (i.e., [[ellipse]], [[parabola]] or [[hyperbola]]) and joined by line segments in any order to form a [[hexagon]], then the three pairs of opposite [[Edge (geometry)|sides]] of the hexagon ([[extended side|extended]] if necessary) meet in three points which lie on a straight line, called the '''Pascal line''' of the hexagon.

The theorem is also valid in the [[Euclidean plane]], but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel.