What is a convex polygon?
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon. Equivalently, it is a simple polygon whose interior is a convex set.
A concave polygon is defined as a polygon with one or more interior angles greater than 180°. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon. Note that a triangle (3-gon) can never be concave. A concave polygon is the opposite of a convex polygon. See Convex Polygon.
- Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting.
- A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note that a triangle (3-gon) is always convex.
- curving or bulging outwards. physics having one or two surfaces curved or ground in the shape of a section of the exterior of a sphere, paraboloid, ellipsoid, etca convex lens. maths (of a polygon) containing no interior angle greater than 180°
Concave is an adjective that describes a surface that curves inward, or is thinner in the middle than on the edges. In ordinary usage, concave and convex are typically used when referring to glass surfaces, like the lenses of optical viewing equipment. The side mirror of a car has a concave surface.
- A concave meniscus, which is what you normally will see, occurs when the molecules of the liquid are attracted to those of the container. This occurs with water and a glass tube. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container, as with mercury and glass.
- Nearsighted people (people who see close objects fine but distant objects appear blurry) have concave lenses in their glasses to correct their vision. A convex lens is thinner at the edges and thicker towards the center. Convex lenses are bent towards a central point.
- In mathematics, a real-valued function defined on an n-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.
A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Take note of what it takes to make the polygon either convex or concave. Also change the number of sides.
- A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than . An example of a non-simple (self-intersecting) polygon is a star polygon. A concave polygon must have at least four sides.
- In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.
- Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. The polygon in Figure 1 has seven sides, so using Theorem 39 gives: An exterior angle of a polygon is formed by extending only one of its sides.
Updated: 3rd December 2019