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1.2 - Notes - Parallel Lines
1.2 - Notes - Parallel Lines

Geometry Name Postulates, Theorems, Definitions, and Properties
Geometry Name Postulates, Theorems, Definitions, and Properties

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Barycentric Coordinates in Olympiad Geometry

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Answers to Geometry Unit 1 Practice

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Handout on Axioms

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10 Geometry Vocabulary Pre/Post Test Name 1 an angle with

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Geometry - 6.5 - Consequences of the Triangle Sum Theorem

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The discovery of non-Euclidean geometries

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Clever Catch - American Educational Products

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Critical - Archdiocese of Chicago

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3-4 companion notes

Assignment 2F Deductive Reasoning, Chain Rule Period ______ Date
Assignment 2F Deductive Reasoning, Chain Rule Period ______ Date

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Duality (projective geometry)

In geometry a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language (§ Principle of Duality) and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a duality. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry.
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