What does convex mean in mathematics?
A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval. More generally, a function is convex on an interval if for any two points and in and any where , (Rudin 1976, p. 101; cf.
What is convex and concave in mathematics?
A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point.
What is definition of convexity?
: the quality or state of being curved outward : the quality or state of being convex. : a shape that is curved outward : a convex shape. See the full definition for convexity in the English Language Learners Dictionary.
What is convex example?
A convex shape is a shape where all of its parts “point outwards.” In other words, no part of it points inwards. For example, a full pizza is a convex shape as its full outline (circumference) points outwards.
How do you know if a figure is convex?
If our shape is a polygon, we can also determine if it is convex by looking at its interior angles. If each of its interior angles are less than or equal to 180 degrees, then the polygon is convex. Functions can also be classified as convex when its slope is increasing.
What is concave in math?
Definition of Concave Concave describes shapes that curve inward. A concave is a surface or a line that is curved inward. In geometry, it is a polygon with at least one interior angle greater than 180°.
What is convex in science?
1. curving or bulging outwards. 2. (General Physics) physics having one or two surfaces curved or ground in the shape of a section of the exterior of a sphere, paraboloid, ellipsoid, etc: a convex lens.
What is convex to the origin?
“Mathematically, a ‘convex to the origin’ curve is described by saying that if A and B are any two points on the curve, then a ray passing through the origin O and any point X on the line segment AB will meet the curve at most at one point D between O and X”.
What is convex area?
the ‘convexArea’ property corresponds the area of the convex hull of the region. The convex area is by definition greater than or equal to the area of the region. It can be used to compute a shape factor known either as “convexity” or “solidity”, defined as the ratio of area over convex area.
Is a circle a convex shape?
The interiors of circles and of all regular polygons are convex, but a circle itself is not because every segment joining two points on the circle contains points that are not on the circle. To prove that a set is convex, one must show that no such triple exists.
How does a convex look?
A convex shape is the opposite of a concave shape. It curves outward, and its middle is thicker than its edges. If you take a football or a rugby ball and place it as if you’re about to kick it, you’ll see that it has a convex shape—its ends are pointy, and it has a thick middle.
What is difference between convex and concave?
Concave describes shapes that curve inward, like an hourglass. Convex describes shapes that curve outward, like a football (or a rugby ball).
What does convex mean in math?
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations. More specifically, in a Euclidean space , a convex region is a region where, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region.
What is the difference between concave and convex geometry?
In geometry, concave and convex refer to polygons. A concave polygon has at least one angle greater than 180 degrees. A convex polygon is made of angles each less than or equal to 180 degrees.
What is the definition of convex in geometry?
Jump to navigation Jump to search. In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space .
What is the meaning of convex?
Use convex in a sentence. adjective. The definition of convex is curving outwards like the edge of a circle. An example of convex is the shape of the lens in eyeglasses.