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Chapter 5: Poincare Models of Hyperbolic Geometry
Chapter 5: Poincare Models of Hyperbolic Geometry

... The fractional linear transformation, T , is usually represented by a 2 × 2 matrix ...
2nd Unit 3: Parallel and Perpendicular Lines
2nd Unit 3: Parallel and Perpendicular Lines

Geometry Chapter 3: Parallel and Perpendicular Lines Term Example
Geometry Chapter 3: Parallel and Perpendicular Lines Term Example

... Corresponding Angles - Angles that lie on the same side of the transversal t, on the same sides of lines r and s. Alternate Interior Angles - Nonadjacent angles that lie on opposite sides of the transversal t, between lines r and s. Alternate Exterior Angles – Angles that lie on opposite sides of th ...
Axioms Corollaries
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... Axiom 1: There is exactly one line through any two given points Axiom 2: [Ruler Axiom]: The properties of the distance between points. Axiom 3: Protractor Axiom (The properties of the degree measure of an angle). Axiom 4: Congruent triangles conditions (SSS, SAS, ASA) Axiom 5: Given any line l and a ...
Parallel and Perpendicular Lines
Parallel and Perpendicular Lines

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... 2. show that A (-1, -3, 4), B (7, -4, 7) and D (1, -6, 10 from a rhombus. 3. Find the direction cosines l, m, n of two lines which are connected by the relations l + m + n = 0 and mn – 2nl – 2lm = 0. 4. Lines OA, OB are drawn from O with direction cosines proportional to 1, -2, -1; 3, -2, 3. Find th ...
Unit 1 Lessons Aug. 2015 - Campbell County Schools
Unit 1 Lessons Aug. 2015 - Campbell County Schools

Q4 - Franklin County Community School Corporation
Q4 - Franklin County Community School Corporation

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Honors Geometry Learning Outcomes

... The fundamental purpose of the course in Geometry is to formalize and extend students’ geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important di ...
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Modern geometry 2012.8.27 - 9. 5 Introduction to Geometry Ancient

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Final Exam Review Ch. 5

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Parallel Lines and Planes

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... given their equations G.G.64 Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line G.G.65 Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line G.G.70 Solve systems of equations invol ...
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End of Module Study Guide: Concepts of Congruence Rigid Motions

... Alternate Interior Angles:  Angles  on  opposite  sides  of  the  transversal  on  the   inside  of  the  parallel  lines.    Alternate  interior  angles  are  congruent  because  you  can   map  one  to  another  by  rotating  180°  arou ...
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Lesson 7A: Solve for Unknown Angles—Transversals

Surface Area and Volume of Spheres
Surface Area and Volume of Spheres

Hyperbolic
Hyperbolic

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Title of Lesson: Introducing Lines Cut By a Transversal Subject

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Parallel Lines and Transversals
Parallel Lines and Transversals

... Parallel Lines and Transversals Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. ...
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Math 3329-Uniform Geometries — Lecture 13 1. A model for

... clear which geometry Riemann actually had in mind. From Riemann’s point of view, in fact, they are simply different spaces with the same geometry, so he may have actually been talking about both. 2. The Models for Elliptic Geometry Axioms will begin fade into the background for us now, and what a sy ...
Name - Harmony
Name - Harmony

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Riemannian connection on a surface



For the classical approach to the geometry of surfaces, see Differential geometry of surfaces.In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form . These concepts were put in their final form using the language of principal bundles only in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked in this modern framework, which provides the natural setting for the classical theory of the moving frame as well as the Riemannian geometry of higher-dimensional Riemannian manifolds. This account is intended as an introduction to the theory of connections.
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