Convex Geometry

Convex geometry is a branch of mathematics that studies shapes known as convex sets. A shape is convex if, for any two points within it, the straight line connecting them lies entirely inside the shape. For example, a circle or a square is convex, while a crescent moon shape is not. This field examines properties and relationships of these shapes, such as their dimensions, volume, and surface area, and has applications in optimization, computer graphics, and economics, helping us understand and analyze multi-dimensional spaces and the behavior of various geometric configurations.