• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Sign in Sign up
Upload
Foundations of Geometry
Foundations of Geometry

Assignments Quadrilaterals
Assignments Quadrilaterals

... 3. In parallelogram ABCD, mA = 2x + 20 and mB = 4x – 50. Find the value of x and determine whether ABCD is a rectangle. Give a reason. 4. In rectangle ABCD, the diagonals AC and BD intersect at E. If AE = 3x + y, BE = 4x – 2y, CE = 20, find the values of x and y. 5. Which of the following is not s ...
Here - Ohio University
Here - Ohio University

Geometry - Hickman County Schools
Geometry - Hickman County Schools

... 3108.4.21 Use properties of and theorems about parallel lines, perpendicular lines, and angles to prove basic theorems in Euclidean geometry (e.g., two lines parallel to a third line are parallel to each other, the perpendicular bisectors of line segments are the set of all points equidistant from t ...
Regular
Regular

Spring 2007 Math 330A Notes Version 9.0
Spring 2007 Math 330A Notes Version 9.0

501 Geometry Questions
501 Geometry Questions

Exploring Triangle Centers in Euclidean Geometry with the
Exploring Triangle Centers in Euclidean Geometry with the

Geometry EOC Assessment Test Item Specifications, Version 2
Geometry EOC Assessment Test Item Specifications, Version 2

Geometry and axiomatic Method
Geometry and axiomatic Method

... B. C. He insisted that, geometric statements must be established by deductive reasoning rather than by trial and error. He was familiar with the computations recorded from Egyptian and Babylonian mathematics, and he developed his logical geometry by determining which results were correct. The next m ...
Document
Document

... 2. All even numbers are divisible by 2. 3. Determine if the statement “If n2 = 144, then n = 12” is true. If false, give a counterexample. ...
Skills Practice Workbook - McGraw Hill Higher Education
Skills Practice Workbook - McGraw Hill Higher Education

From Hilbert to Tarski - HAL
From Hilbert to Tarski - HAL

... First, we had to change the lower dimensional axiom. Hilbert states that there exists three non collinear points and three points are said to be collinear if there exists a line going through these three points. This assumption is not enough, because in a world without lines, assuming that there are ...
Constructive Geometry and the Parallel Postulate
Constructive Geometry and the Parallel Postulate

Constructive Geometry and the Parallel Postulate
Constructive Geometry and the Parallel Postulate

Tangent circles in the hyperbolic disk - Rose
Tangent circles in the hyperbolic disk - Rose

Geometry - Eleanor Roosevelt High School
Geometry - Eleanor Roosevelt High School

... Let k represent “Kurt plays baseball.” Let a represent “Alicia plays baseball.” Let n represent “Nathan plays soccer.” Write each given sentence in symbolic form: a.Alicia plays baseball or Alicia does not play baseball (a V ~a) b.It is not true that Kurt or Alicia play baseball (~(k V a)) Mr. Chin- ...
Geometry EOI Practice 1. By the Law of Syllogism, what statement
Geometry EOI Practice 1. By the Law of Syllogism, what statement

ISOSPECTRAL AND ISOSCATTERING MANIFOLDS: A SURVEY
ISOSPECTRAL AND ISOSCATTERING MANIFOLDS: A SURVEY

Word - The Open University
Word - The Open University

Geometry - Eleanor Roosevelt High School
Geometry - Eleanor Roosevelt High School

... An indirect proof works because the negation of the statement to be proved is false, then we can conclude that the statement is true ...
Geo 4.3to4.5 DMW
Geo 4.3to4.5 DMW

Contemporary Arguments For A Geometry of Visual Experience
Contemporary Arguments For A Geometry of Visual Experience

... awareness of the shape and location of objects at a distance. However, it would be unwarranted to infer from this alone that what it is like to see by means of sonar is the same as what it is like to see by means of eyes. For example, the geometry could be different, even though the topology is not, ...
Proving that a Quadrilateral is a Parallelogram Any of the methods
Proving that a Quadrilateral is a Parallelogram Any of the methods

... Name Honors Geometry Given: CirCle H and CirCle "Prove: HELO is a parallelogram ...
X - Ms. Williams – Math
X - Ms. Williams – Math

1 2 3 4 5 ... 32 >

Cartan connection

In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan connections describe the geometry of manifolds modelled on homogeneous spaces.The theory of Cartan connections was developed by Élie Cartan, as part of (and a way of formulating) his method of moving frames (repère mobile). The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. For instance, in relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection.Cartan reformulated the differential geometry of (pseudo) Riemannian geometry, as well as the differential geometry of manifolds equipped with some non-metric structure, including Lie groups and homogeneous spaces. The term Cartan connection most often refers to Cartan's formulation of a (pseudo-)Riemannian, affine, projective, or conformal connection. Although these are the most commonly used Cartan connections, they are special cases of a more general concept.Cartan's approach seems at first to be coordinate dependent because of the choice of frames it involves. However, it is not, and the notion can be described precisely using the language of principal bundles. Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method of moving frames, Cartan connection applications and Einstein–Cartan theory for some examples.
  • studyres.com © 2023
  • DMCA
  • Privacy
  • Terms
  • Report