Definition:Convex Polygon/Definition 4

This article needs to be linked to other articles. In particular: throughout You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. 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 {{MissingLinks}} from the code.

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

• Results about convex polygons can be found here.

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.