Convex bodies

A convex body is a shape in which, if you pick any two points inside it and draw a straight line between them, the entire line stays inside the shape. Imagine a rubber band stretched around various objects; if it can surround them completely without bulging inward, those objects are convex. Common examples include circles, spheres, and cubes. In contrast, a shape with indentations or holes, like a crescent moon, is not convex. Convex bodies are significant in mathematics, geometry, and various fields, as they simplify analysis and optimization problems.