Fenchel's theorem

Fenchel's theorem states that for any closed space curve—imagine a loop in three-dimensional space—the total curvature (a measure of how much the curve bends) is at least 4π (about 12.57). In simple terms, the more a loop twists and turns in space, the greater its total bending. This is a fundamental result in differential geometry, ensuring that tight or complex loops must bend sufficiently, with the minimal total bending occurring in a perfect circle, which has a total curvature of exactly 2π. The theorem connects the shape of a loop with its overall bending behavior in three-dimensional space.