convex polygon
a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon
A convex polygon is a polygon with all of its interior angles less than 180 degrees. In other words, all the vertices of a convex polygon point outwards. Convex polygons are important in various fields of mathematics, geometry, and design.
Examples of convex polygons are triangles, rectangles, pentagons, hexagons, heptagons, and so on. They are used to model and represent various shapes and structures, such as buildings, furniture, and machine parts.
One of the essential properties of a convex polygon is that its opposite sides are parallel and equal in length. Additionally, the sum of its interior angles is equal to (n-2) * 180 degrees, where n is the number of sides.
Convex polygons are also useful in optimization problems because they allow for efficient and scalable computations. For example, suppose you want to find the shortest route that passes through a number of points. You can represent the points as vertices of a convex polygon, and the shortest path will be the perimeter of the polygon.
In conclusion, a convex polygon is a polygon whose interior angles are less than 180 degrees. They are important in various fields of mathematics, geometry, and design and have useful properties in optimization problems.
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