In projective geometry, Pascal's theorem (aka Hexagrammum Mysticum Theorem) states that if an arbitrary six points are chosen on a 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 sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon. The theorem is valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel.
Read more about Pascal's Theorem: Euclidean Variants, Related Results, Hexagrammum Mysticum, Proofs, Proof Using Cubic Curves, Proof Using Bézout's Theorem
Famous quotes containing the words pascal and/or theorem:
“Knowledge has two extremes. The first is the pure natural ignorance in which all men find themselves at birth. The other extreme is that reached by great minds, who, having run through all that men can know, find they know nothing, and come back again to that same natural ignorance from which they set out; this is a learned ignorance which is conscious of itself.”
—Blaise Pascal (1623–1662)
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