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Two ears theorem

In geometry, the two ears theorem states that every simple polygon with more than three vertices has at least two ears, vertices that can be removed from the polygon without introducing any crossings. The two ears theorem is equivalent to the existence of polygon triangulations. It is frequently attributed to Gary H. Meisters, but was proved earlier by…

Statement of the theorem, Relation to triangulations & Related types of vertex

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Statement of the theorem

Simple closed curveEuclidean planeLine segmentsJordan curve theorem
4 related topics

Relation to triangulations

TriangleWeak dualTreeLinear time
4 related topics

Related types of vertex

Convex hullAnthropomorphic polygons
2 related topics

Overview

GeometrySimple polygonEarsPolygon triangulationsMax Dehn
5 related topics

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Overview

Statement of the theorem

Relation to triangulations

Related types of vertex

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Map overview Semantic statistics

Two ears theorem

Nodes20
Edges19
Triples28
Avg. degree1.9
Density0.1
Components1

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Two ears theorem

Top relations

related to Related types of vertex · 8
Two ears theorem → An, Analogously, Ears, However, Polygons, Removing, Repeatedly, This
related to Relation to triangulations · 8
Two ears theorem → Although, An, By, Conversely, Removing, Since, Thus, Triangulation
related to history · 7
Two ears theorem → Dehn's, Gary, However, Jordan, Max Dehn, Meisters, The
related to Statement of the theorem · 5
Two ears theorem → An, By, Euclidean, Jordan, The

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Important terminology

polygon ears two theorem ear triangle simple vertices vertex convex every triangulated displaystyle least line one neighbors triangulation mouth consecutive

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Two ears theoremrelated to historyThe0.60section
Two ears theoremrelated to historyGary0.60section
Two ears theoremrelated to historyMeisters0.60section
Two ears theoremrelated to historyHowever0.60section
Two ears theoremrelated to historyMax Dehn0.60section
Two ears theoremrelated to historyJordan0.60section
Two ears theoremrelated to historyDehn's0.60section
Two ears theoremrelated to Related types of vertexAn0.60section
Two ears theoremrelated to Related types of vertexHowever0.60section
Two ears theoremrelated to Related types of vertexEars0.60section
Two ears theoremrelated to Related types of vertexAnalogously0.60section
Two ears theoremrelated to Related types of vertexPolygons0.60section

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    Min side: 3
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