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Abstract
The radius of gyration of a space curve is a measure of how tightly wound that curve is. In recent years, it has gained usage by molecular biologists investigating the geometric aspects of protein folding. Here, we explore the radius of gyration of sufficiently smooth space curves, primarily focusing on criticality. We use the calculus of variations to define criticality for the radius of gyration, then show that among curves of a fixed length, only a curve which is a straight line segment is critical.