Definition:Duality (Geometry)

Definition

Duality in the context of geometry is a property that conceptually connects types of object with other types of object.

Plane Geometry

In the context of plane geometry, the straight line and the point are dual elements:

a straight line can be defined by two points

a point can be defined by the intersection of two straight lines.

Solid Geometry

In the context of solid geometry, the plane and the point are dual elements:

a plane can be defined by two straight lines

a point can be defined by the intersection of two straight lines.

Also see

• Definition:Dual Elements
• Definition:Dual Operations
• Definition:Dual Statements
• Principle of Duality

• Results about duality in the context of geometry can be found here.

Sources

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