No, the region enclosed by a circle is not considered convex because it contains points within the circle that do not lie on the boundary of the circle. In convex regions, any line segment connecting two points inside the region will also lie completely inside the region.
Yes, in optimization problems, the feasible region must be a convex set to ensure that the objective function has a unique optimal solution. This is because convex sets have certain properties that guarantee the existence of a single optimum within the feasible region.
A magnifying glass is convex.
The human eye has a double convex lens in the cornea (outermost layer) and a bi-convex lens in the crystalline lens inside the eye.
The region of the world where it is light 24 hours a day is the Arctic Circle during the summer months.
Flashlights typically have a convex lens. A convex lens is thicker in the middle and thinner at the edges, which helps to converge the light rays and create a focused beam.
Yes.
Sector
convex
no
A part of a circle enclosed by two radii is called a sector.
It is a sector of the circle
Area of a sector of a circle.
Exactly as in the question and a segment of a circle is the area enclosed by a chord and an arc of a circle.
A sector of a circle is the region enclosed by two radii and the circumference. If you draw a picture, you can see that there are actually two regions formed. One has an angle of 180 degrees or less at the center, and the other has an angle of 180 degrees or more. A sector which occupies more than half of the circle is a major sector. To put it more succinctly, a major sector is enclosed by two radii and a major arc of a circle.
Convex Polygon
A star or enclosed circle
Yes, in optimization problems, the feasible region must be a convex set to ensure that the objective function has a unique optimal solution. This is because convex sets have certain properties that guarantee the existence of a single optimum within the feasible region.