Pascal's Mystic Hexagram

Theorem

Let $ABCDEF$ be a hexagram whose $6$ vertices lie on an ellipse such that the order of vertices along the ellipse is $AECFBD$.

Then the points of intersection of the sides of $ABCDEF$ lie on a straight line.

Proof

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Also see

• Pappus's Hexagon Theorem
• Desargues' Theorem
• Pascal's Theorem

Source of Name

This entry was named for Blaise Pascal.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9$