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Suppose you have any ellipse.
Choose any six distinct points on the ellipse, and form a hexagon by
connecting the six points, in order, with straight-line segments. As
discussed in Menelaus' Theorem above, each of these line segments has
an extension that passes through a consecutive pair of points, but extends
to infinity. Pascal's Mystic Hexagram Theorem guarantees that the points
of intersection of the extensions of the opposite sides of the hexagram
must lie on the same line. (If you are confused about the term "opposite
sides', consider numbering the sides, in order, from 1 through 6; then
side 1 is opposite side 4, side 2 is opposite side 5, and side 3 is
opposite side 6.)
Blaise Pascal presented this
theorem, with a proof, when he was just 16 years old, in approximately
1638.
Similar to that for Desargues
Theorem.
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