isoperimetric problem

The isoperimetric problem involves finding the shape that encloses a fixed area with the least possible perimeter or boundary length. In simple terms, it asks: among all shapes with the same area, which one has the smallest perimeter? The classic answer is a circle—because it encloses a given area most efficiently, with the shortest boundary length. This problem helps mathematicians understand optimal shapes and has applications in fields like physics, engineering, and biology, where efficiency in boundary lines or surfaces is important.