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Simple polygon: Definitions, Computational problems & Overview

In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons.

Language: English [EN]
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Simple polygon topic overview

The analysis highlights Definitions, Computational problems and Overview as prominent areas in the source structure around Simple polygon.

Related topics
62
Source areas
5
Connected nodes
67
Extracted relationships
42
Concept neighborhoods
33
Bridge connections
67

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 22 topics
Definitions · 16 topics
Computational problems · 13 topics
Properties · 7 topics
Related constructions · 4 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definitions

Properties

Computational problems

Related constructions

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Simple polygon connects Entity context

The extracted context around Simple polygon shows recurring relationship patterns in the source. For example, Simple polygon → Although, Constructing, In, It, NP-complete, Pick's, Point, Simple, The, These, This Another extracted example is Simple polygon → An, Edges, Euclidean, No, Some, The, Two. Use these groups to spot repeated connection types before inspecting the individual relationships.

Simple polygon

Top relations

related to Computational problems · 11
Simple polygon → Although, Constructing, In, It, NP-complete, Pick's, Point, Simple, The, These, This
related to Definitions · 7
Simple polygon → An, Edges, Euclidean, No, Some, The, Two
related to Related constructions · 7
Simple polygon → According, Christoffel, Connecting, Every, Riemann, Schwarz, These
related to Properties · 6
Simple polygon → Every, For, If, The, Thus, When
related to External links · 4
Simple polygon → Eric, MathWorld, Simple, Weisstein
related to Special cases · 3
Simple polygon → Another, Equivalently, Every
is a · 2
Simple polygon → closed curve in the Euclidean plane consisting of straight line segments, polygon that does not intersect itself and has no holes
see also · 2
Simple polygon → Carpenter's, Nagy

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

polygon simple vertices displaystyle line interior point polygons every vertex two one theorem convex points sides time segments geometry also

Simple polygon relationships Subject–Predicate–Object triples

TTTA extracted 42 structured relationships around Simple polygon. Examples in this analysis include Simple polygon → is a → polygon that does not intersect itself and has no holes and Simple polygon → is a → closed curve in the Euclidean plane consisting of straight line segments. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Simple polygonis apolygon that does not intersect itself and has no holes0.90text
Simple polygonis aclosed curve in the Euclidean plane consisting of straight line segments0.90text
Simple polygonrelated to Computational problemsIn0.60section
Simple polygonrelated to Computational problemsPoint0.60section
Simple polygonrelated to Computational problemsIt0.60section
Simple polygonrelated to Computational problemsSimple0.60section
Simple polygonrelated to Computational problemsThese0.60section
Simple polygonrelated to Computational problemsPick's0.60section
Simple polygonrelated to Computational problemsThe0.60section
Simple polygonrelated to Computational problemsConstructing0.60section
Simple polygonrelated to Computational problemsThis0.60section
Simple polygonrelated to Computational problemsAlthough0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Simple polygon bring nearby vocabulary together. In this analysis, examples include Simple, Interior and Displaystyle. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Simple polygon
    • Simple
    • Interior
    • Displaystyle
    • Polygons
    • Vertices
    • Every
    • Theorem
    • Line
    • Point
    • Also
    • Sides
    • Angles
  • simple polygon
    • Simple
    • Interior
    • Displaystyle
    • Vertices
    • Polygons
    • Every
    • Theorem
    • Line
    • Point
    • Time
    • Two
    • Also
  • polygon
    • Simple
    • Interior
    • Displaystyle
    • Vertices
    • Every
    • Line
    • Time
    • Two
    • Sides
    • Points
    • One
    • Point
  • line segments
    • Segments
    • Segment
    • Interior
    • Form
    • Points
    • Polygon
    • Every
    • Two
    • Plane
    • Set
    • Simple
    • Given
  • convex polygons
    • Polygons
    • Theorem
    • Point
    • Simple
    • Vertex
    • Include
    • Computational
    • Segment
    • Given
    • Used
    • Called
    • Polygon
  • computational geometry
    • Computational
    • Geometry
    • Form
    • Given
    • Convex
    • Polygons
    • Simple
    • Point
    • Area
    • Graph
    • Include
    • External
  • point in polygon
    • Simple
    • Visible
    • Interior
    • Displaystyle
    • Vertices
    • Polygons
    • Given
    • Every
    • Line
    • Time
    • Two
    • Points
  • convex hull of a simple polygon
    • Simple
    • Interior
    • Polygons
    • Displaystyle
    • Vertices
    • Vertex
    • Every
    • Include
    • Theorem
    • Line
    • Point
    • Time

Connections between topic areas Semantic bridges

For Simple polygon, one of the stronger structural bridges in this analysis connects Simple polygon with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Simple polygonOverview · splits 45 ⟂ 23
Simple polygonDefinitions · splits 51 ⟂ 17
Simple polygonComputational problems · splits 54 ⟂ 14
Simple polygonProperties · splits 60 ⟂ 8
Simple polygonRelated constructions · splits 63 ⟂ 5

Map overview Semantic statistics

Simple polygon

Nodes68
Edges67
Triples42
Avg. degree1.97
Density0.029412
Components1

Source & methodology

TTTA analyzes the structure around Simple polygon to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definitions, Computational problems & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Simple polygon · EN edition · Analysis: TopicsToTalkAbout

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