• 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
computational
computational

A CGAL implementation of the Straight Skeleton of a - DMA-FI
A CGAL implementation of the Straight Skeleton of a - DMA-FI

... instants of the events) and constructions (for bisectors and events). As with most geometric algorithms, its correctness can be made a exclusive function of its predicates if these are chosen carefully. In our case, the fundamental predicates are the relative ordering of events. It suffices that the ...
Solution
Solution

... 1. a1 a2 a3 and a3 a2 a1 are two three-digit decimal numbers, with a1 , a3 being different non-zero digits. The squares of these numbers are five-digit numbers b1 b2 b3 b4 b5 and b5 b4 b3 b2 b1 respectively. Find all such threedigit numbers. Solution. Assume a1 > a3 > 0. As the square of a1 a2 a3 mu ...
geometry – first semester exam review
geometry – first semester exam review

Geometry 2.1.3 Class Exploration #25 Suppose a in the diagram
Geometry 2.1.3 Class Exploration #25 Suppose a in the diagram

Perpendicular transversal Theorem
Perpendicular transversal Theorem

Name: _______________________ corresponding < are congruent
Name: _______________________ corresponding < are congruent

Alternating Paths through Disjoint Line Segments
Alternating Paths through Disjoint Line Segments

... Michael Hoffmann and Csaba D. Tóth Institute for Theoretical Computer Science ...
Name: TP: ____ CRS PPF 601 – Apply properties of 30-60
Name: TP: ____ CRS PPF 601 – Apply properties of 30-60

File
File

File
File

Higher
Higher

6_1 Practice B
6_1 Practice B

Minimal tangent visibility graphs
Minimal tangent visibility graphs

... hull of the obstacles are edges of any pseudo-triangulation. A pseudo-triangulation of a collection of six obstacles is depicted in Fig. 3. L e m m a 2.1. The bounded free faces of any pseudo-triangulation are pseudotriangles. Proof. Let B be a family of noncrossing bitangents containing the bitange ...
LESSON 4-1: CONGRUENT FIGURES/POLYGONS
LESSON 4-1: CONGRUENT FIGURES/POLYGONS

... POLYGON: A polygon is a closed plane figure formed by three or more segments. Each segment intersects exactly two other segments, but only at their endpoints, and no two segments with a common endpoint are collinear. The vertices of the polygon are the endpoints of the sides. When naming a polygon, ...
Sect8-3-5 - epawelka-math
Sect8-3-5 - epawelka-math

Andrej Risteski - The Program in Applied and Computational
Andrej Risteski - The Program in Applied and Computational

The Complete Mathematical Terms Dictionary Understanding math
The Complete Mathematical Terms Dictionary Understanding math

5-2 bisectors of triangles
5-2 bisectors of triangles

Two-Dimensional Figures
Two-Dimensional Figures

Slide 1 - cristama wiki
Slide 1 - cristama wiki

Notes 4B: Triangle Angle Measures Vocabulary
Notes 4B: Triangle Angle Measures Vocabulary

Presentation Notes
Presentation Notes

Eight circle theorems page
Eight circle theorems page

Solutions - Austin Mohr
Solutions - Austin Mohr

< 1 ... 36 37 38 39 40 41 42 43 44 ... 63 >

Steinitz's theorem



In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices). That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who submitted its first proof for publication in 1916. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name ""Steinitz's theorem"" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report