• 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 →
 
Profile Documents Logout
Upload
6-3 - Spring Branch ISD
6-3 - Spring Branch ISD

... using the definition of parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0). ...
lesson 1.3 Geometry.notebook
lesson 1.3 Geometry.notebook

τ* -Generalized Compact Spaces and τ* -Generalized
τ* -Generalized Compact Spaces and τ* -Generalized

Geometry Essential Curriculum
Geometry Essential Curriculum

Geometry 1
Geometry 1

... a line segment, the distance formula, and various forms of equations of lines and circles. ...
Tychonoff`s Theorem Lecture
Tychonoff`s Theorem Lecture

Math 535 - General Topology Fall 2012 Homework 8 Solutions
Math 535 - General Topology Fall 2012 Homework 8 Solutions

Elements of Homotopy Fall 2008 Prof. Kathryn Hess Series 13 Let B
Elements of Homotopy Fall 2008 Prof. Kathryn Hess Series 13 Let B

Pairs of Pants and Congruence Laws of Geometry - Rose
Pairs of Pants and Congruence Laws of Geometry - Rose

Chapter 3: Topology of R Dictionary: Recall V ε(x) is the open
Chapter 3: Topology of R Dictionary: Recall V ε(x) is the open

... [At this point students are ready to do the sixth problem set.] Optional: Topology in general: Topology (or “rubber-sheet geometry”) is a major field of study in math. The most active areas are probably in “manifolds”, where every point has a neighborhood that looks like a neighborhood in some Rn . ...
Angle Relationships in Triangles
Angle Relationships in Triangles

Compactness 1
Compactness 1

MATH 521, WEEK 7: Open Covers, Compact Sets
MATH 521, WEEK 7: Open Covers, Compact Sets

REGULAR CONVERGENCE 1. Introduction. The
REGULAR CONVERGENCE 1. Introduction. The

... 1. Introduction. The notion of convergence is certainly one of the most important ones in all mathematics. In analysis if a sequence of functions converges to a limit function, we ask the question what properties enjoyed by the members of the sequence are carried over to the limit function. With no ...
Basic Notions Of Topology
Basic Notions Of Topology

... A system B of open subsets of a topological space (X, O) ist called an open basis of the topology, if every open set O ∈ O is the union of sets from B, i.e. for all O ∈ O holds: ∀ x ∈ O ∃ B ∈ B : B ⊂ O and x ∈ B. An open subbasis of (X, O) is a system S ⊂ O such that the set of all finite intersecti ...
Triangles Unit Guide Geometry
Triangles Unit Guide Geometry

... Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. See High School Flip Book page 157 for explanations and examples of this standard. Learning Objectives  Students will be able to formally construct using a variety of tools and me ...
5-6: Proving Lines Parallel Day 2
5-6: Proving Lines Parallel Day 2

Definitions.
Definitions.

An introduction to differential topology
An introduction to differential topology

PDF
PDF

PDF
PDF

Advanced Geometry
Advanced Geometry

Geometry - USD 489
Geometry - USD 489

Geometry - BAschools.org
Geometry - BAschools.org

March Regional
March Regional

... investigation—a pass code you have deduced to be ABCD. Your subordinates have given you four clues they found in their own investigations, as follow: A = the sum of the digits of the sum of the exterior angles of a regular icosagon. B = the number of sides of the largest regular polygon that can tes ...
< 1 ... 83 84 85 86 87 88 89 90 91 ... 153 >

Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply-connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic).In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982), and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print.Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.There are now several different manuscripts (see below) with details of the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report