If six points lie on a conic section, the three intersection points of the three pairs of opposite sides of the hexagon they form are collinear. Discovered by Blaise Pascal at age sixteen, it generalizes Pappus's theorem to conics.
Facts
StatementIf six points on a conic section are joined in any order to form a hexagon, the three pairs of opposite sides of the hexagon, extended if necessary, meet at three points that lie on a single straight line, the Pascal line. 1 Proof YearFormulated in a note Pascal wrote in 1639 at age 16; published the following year, 1640, as the broadside Essay pour les coniques. Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Pascal's Theorem (Wikipedia)
Wikimedia FoundationLead section, opening theorem statement
If six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) 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 at three points which lie on a straight line, called the Pascal line of the hexagon.
Lead section, sentence on Pascal's 1639/1640 dating
It was formulated by Blaise Pascal in a note written in 1639 when he was 16 years old and published the following year as a broadside titled 'Essay pour les coniques. Par B. P.'
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