Definition:Convex Polygon/Definition 4

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Definition

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

the region enclosed by $P$ is the intersection of a finite number of half-planes.

Note that an intersection of a finite number of half-planes is not necessarily a polygon.

This page has been identified as a candidate for refactoring of medium complexity. In particular: This is to be repurposed as an equivalence proof. To define a polygon in such a manner is of questionable merit. To treat it as a characteristic of a convex polygon makes more sense. Please see the section in the house style guide about how to determine whether a characterising property should be presented as a definition page or a characteristic page, that is, something like: "Polygon is Convex iff Intersection of Finite Number of Half-Planes". Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code.

Also see

• Equivalence of Definitions of Convex Polygon

Sources

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