Review: Points, Lines, Planes, and Angles
Review: Points, Lines, Planes, and Angles

Solutions - UBC Math
Solutions - UBC Math

... points at x = 1, 3. We should note that while (x − 1)(x − 3) will work, any multiple of that will also work. For example, solving for g(x) − x = −4(x − 1)(x − 3) will yield a different (but also correct) quadratic with fixed points at x = 1, 3. A similar justification is required to show that these ...
geo journal
geo journal

... Ray: A line that has a starting point and in one side it keeps on going forever and in the other side, it stops. Ex: The three of them join two points however, some stop and other continues their path. ...
microsoft word document
microsoft word document

Geometry Fall 2015 Lesson 046
Geometry Fall 2015 Lesson 046

Geometry: Mr. Miller`s Class – Lesson Ch 1.1 Identify Points, Lines
Geometry: Mr. Miller`s Class – Lesson Ch 1.1 Identify Points, Lines

Unit 1
Unit 1

Counter Examples To show that a statement is false it is enough to
Counter Examples To show that a statement is false it is enough to

Chapter 3 3379
Chapter 3 3379

Sample
Sample

... 2222: The region is defined by the four lines through two copies of two points of rotations by π. Note the other two rotations are also on the lines. This forms a quadrilateral. o: The region is defined by two copies of each of the vectors. These form a parallelogram (quadrilateral). *X: The region ...
Unit 4 Review
Unit 4 Review

Unit 2 Geometry vocabulary list
Unit 2 Geometry vocabulary list

Unit 7 KUDOs Name Math 8 Essential Questions: What is similarity
Unit 7 KUDOs Name Math 8 Essential Questions: What is similarity

2.5 Perpendicular Lines
2.5 Perpendicular Lines

Unit Title: Suggested Time
Unit Title: Suggested Time

... (2) When lines intersect a circle or within a circle, how do you find the measures of resulting angles, arcs, and segments? (3) How do you find the equation of a circle in the coordinate plane? (4) How is each conic section formed by passing a plane through a cone? (5) Given the equation of a circle ...
Negation-writing the negative of the statement
Negation-writing the negative of the statement

Unit 1 Analogies
Unit 1 Analogies

Geometry Name: Date:______ Period:_____ WS 1.2
Geometry Name: Date:______ Period:_____ WS 1.2

Chapter 2 Test Review Answer Section
Chapter 2 Test Review Answer Section

Section 3.6
Section 3.6

Poincaré`s Disk Model for Hyperbolic Geometry
Poincaré`s Disk Model for Hyperbolic Geometry

GEOMETRY UNIT 2 TEST REVIEW
GEOMETRY UNIT 2 TEST REVIEW

List of Theorems, Postulates and Definitions 3
List of Theorems, Postulates and Definitions 3

PDF
PDF

Voc
Voc

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.