If p is the perimeter of a closed curve in a plane and the area enclosed by the curve is A, then p²≥4π‎A, and equality is only achieved if the curve is a circle. Turning around this condition, it says that for a fixed length of curve p the greatest area which can be enclosed is when the curve is a circle. The result can be generalized to surfaces in 3‐dimensional space where the sphere is the most efficient shape at enclosing volume for a fixed surface area, and to higher dimensions.