Live briefing
Everything about Two ears theorem
Every simple polygon with more than three vertices has at least two ears
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 Max Dehn. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Two ears theoremA 5-minute orientation
- Skim a recent paper: A Quantified Two-Projection Theorem for Nonlinear ProjectionsInfluential work since 2022
- Pick up a classic book: The Travelling Salesman Problem and Its VariationsThe most-reprinted book on the subject
- Go sideways: Polygon triangulationA closely related topic
- Go sideways: Simple polygonA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
- No matching papers found.
🆕 Influential since 2022
đź“š Books worth reading
The Travelling Salesman Problem and Its VariationsGregory Gutin · 2002
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Polygon triangulation In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of…
- Simple polygon 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…
- Fan triangulation In computational geometry, a fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing edges to all of the other vertices…
- Anthropomorphic polygon In geometry, an anthropomorphic polygon is a simple polygon with precisely two ears and one mouth. That is, for exactly three polygon vertices, the line…
- Convex polygon In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is…
- Vertex (geometry) In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect…
- Art gallery problem The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem:…
- Schönhardt polyhedron In geometry, a Schönhardt polyhedron is a polyhedron with the same combinatorial structure as a regular octahedron, but with dihedral angles that are non-convex…