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:
“The strength of a man’s virtue must not be measured by his efforts, but by his ordinary life.”
—Blaise Pascal (1623–1662)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)