Duality Principle (Projective Geometry)

Theorem

Principle of Duality in the Plane

Let $P$ be a theorem of projective geometry proven using the propositions of incidence.

Let $Q$ be the statement created from $P$ by interchanging:

$(1): \quad$ the terms point and (straight) line

$(2): \quad$ the terms collinear (of points) and concurrent (of lines)

$(3): \quad$ the terms lie on and intersect at

and so on.

Then $Q$ is also a theorem of projective geometry.

Principle of Duality in Space

Let $P$ be a theorem of projective geometry proven using the propositions of incidence.

Let $Q$ be the statement created from $P$ by interchanging:

$(1) \quad$ the terms point and plane

$(2) \quad$ the terms lie on and intersect at

and so on.

Then $Q$ is also a theorem of projective geometry.

Also known as

A Duality Principle is also known as a Principle of Duality.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): duality: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): projective geometry
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): duality: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): projective geometry